Will gradually expand these root explanations to full pages while retaining the concise version. Brief synopses don't really do them justice.

Word Sleuth:
*h2rkos (PIE) - Bear

Old Irish. art, Latin ursus, Greek. αρκτος, Albanian. Ari, Armenian ar, Sanskrit. rksa-.
Neanderthal man stored cave bear skulls in stone cabinets in high caves in Switzerland (Wildkirchli, Drachenloch and Wildenmannlisloch) and Germany (Petershöhle) suggesting a cave bear cult even before the modern version of homo sapiens entered europe about 40,000 years ago. The above root is found in the names of three European cities Berne, Bayern and Verona. The Celtic bear goddess was called, Artio, and young girls in Greece that danced for the goddess, Artemis were called αρκτοι(bears).
The name Arthur derives from the Celtic root, art, was earlier the name of a Celtic god, Ardehe, or Arthe, about 6th century BC, to whom there is an altar inscribed in the town of St. Pé d'Ardet which is situated in the Pyrenees in the Vallée de l'Ourse or Valley of the Bear. Of course the cave bear went extinct short after the period it was painted in the cave of Chauvet in France, maybe 30,000 years ago, and all later references and mythologies refer to the Eurasian Brown Bear.

*h2ster (PIE) - star

Possibly derived from the noun *h2(hx)-s-tér ember or *h&2ehx-s- to burn.
Middle Irish ser star;Latin stēlla star, English star; Greek astēr star; Armenian astl star; Hittite hasterza star and Sanskrit tãras stars.

*méh1-nōt or *meh1-n(è)s (PIE) - moon

The main word for moon derives from the verb, *méh1-, to measure and indicates a functional conception of the moon. The meaning of the reflexes may be moon or month or both.
i.e. Old Irish ; month; Latin mēnsis month; English moon, month; Lithuanian mënuo moon, month; Albanian muaj month;Greek mēn month; Armenian amis month; Avestan moon, month; Sanskrit mãs- moon, month and Tocharian B meñe moon, month.

*séhaul (PIE) - Sun

The word for the Sun is old: Latin sōl sun; English sun; Lithuanian sáulė sun; Greek hēélios; Avestan hvar sun; Sanskrit svàr~ sūr(y)a; the Old Irish cognate sūil means eye, a concept also reprised in both Greek and Indic mythology.
In Eygpt the sun is represented as, N5 , and can also be represented as The Eye of Ra . This is frequently represented in hieroglyphs as the mirror opposite of the more common, Wadjet Eye, D10 , which has lunar associations. Originally the sun and moon were the right and left eyes respectively of Horus as a celestial falcon.
For reference, in China and Japan the basic symbol for the sun is, , and that for the eye,.

Medb (Irish) - goddess/mythic character

The old Irish goddess, and Queen of Connacht in the epic the Taín, name is derived from the root *medhwiha- intoxicator which is cognate with the Sanskrit mãdhavī. See also *mélit for honey and *médhu for mead.

*mélit (PIE) - honey

The PIE noun for honey mélit is mil in Old Irish, mel in Latin, miel in French, melr in Armenian, militt in ancient Hittite and Greek méli. The Chinese word for honey mi - 蜜 is thought to be borrowed from the Proto-Tocharian mit. The name Melissa means Honey Bee in Greek
A cave painting in Valencia Spain, depicts a honey harvester with bees swarming around in Cueve de la Arana (cave of the spider) dating from circa 13,000 BCE.

*lóks (PIE) - salmon

Old English leax salmon, Old High German lahs salmon; Lithuanian lãšis salmon; Tocharian B laks fish.

*dóru (PIE) - Tree

The general name of tree ,*dóru, is attested in eleven different groups, either under its root form: Old Irish oak, daur; Greek treetrunk/wood/spear δορυ (doru); Hittite tree or wood, tãru, Avestan tree/tree trunk/ wooden weapon, dãuru; Sanskrit wood ,dãuru.

Or in derivation: modern English tree; Greek tree/oak δρυσ(drûs); Old Church Slavic (OCS) wood, drûva; Albanian tree/wood , dru and oak drushk; and Sanskrit wood ,dãuru.

While the evidence for the origin of Proto Indo-European points towards the largely treeless Pontic Caspian steppe, it may be signficant that in Celtic and Greek, which cultures gestated within the temperate woodlands of Europe, the root tends to refer specifically to the oak tree and has religious connotations such as the word druid -i.e tree-knower or dryad - tree nymph.

In particular the oak tree is associated with the chief deity of most of the Indo-European peoples who is the yielder of the lightening bolt.(see The Workship of the Oak, Celtic Tree Worship and Sacred Groves).

*médhu (PIE) - mead

A fermented drink made from honey. Old Irish mid, Modern English mead, Latvian medus, Greek méthu -wine, Avestan meθu - berry wine, Sanskrit mádhu - honey / wine.

*weghos (PIE) - way,path

The old PIE root is manifested in English way and German weg. However if we look eastwards, in Sanskrit we have marga. About which, discussing the difference between temporal art and the religious iconography of India's myriad gods and goddesses, Joseph Campbell writes:

In contrast to the figures in works of secular art (desi) they [images of the gods] open the mind to brahman and are know themselves, as the path or the way (marga). The sanskrit marga is derived from mrg, to hunt (by following the track of an animal through the forest to its lair), the animal to be found through contemplation of the image of a god being, of course, that indwelling golden person (purusha) which is one's own eternal portion. (The Way of the Seeded Earth vol1 p29)
Further east we find the notion in Chinese tao or dao, The Way, a comprehensive philosophy of life which unlike the introverted philosophies of India is very much imbued with awe at the physical wonder of the world. Further east again in Japan the word reverts again to many different paths with the word   - dō . It retains its abstract sense and can be found in the names of many disciplines such as Bushidō 武士道 - the Way of the Warrior; Chadō 茶道 - the Way of Tea; Jūdō  柔道  -the Gentle Way; Kendo 剣道  - the Way of the Sword, Aikidō 合気道 - roughly, the Way of Harmonising (with) Life Energy. The indigenous Japanese pantheistic religion is called Shinto 神道, roughly, the way of the spirit/s.
The dash and lower part of the character denotes movement and the right part of the character denotes chief/main. So the kanji in its most prosaic sense means main road.

dhárma (SKT) - moral duty.

In contrast to the oriental idea of marga (SKT) or tao (CH), the Way, there is the more prevalent, and constraining, notion of dhárma, or moral duty. In India this idea depends on a person's age, class, occupation, and gender.
It is a derivation from Proto-Indo-Iranian root *dhar- ("to fasten, to support, to hold"), in turn reflecting Proto-Indo-European root *dher- ("to hold"). Etymologically it is related to Avestan √dar- ("to hold"), Old Persian √dar-("to hold, have"), Latin frēnum ("rein, horse tack"), Lithuanian derė́ti ("to be suited, fit") and Lithuanian dermė (agreement), darna ("harmony").
Further east in China and Japan the best equivalent would probably be the character for law,. In Japanese this can be used to denote the Budda's Law, 仏法 (bupou) or secular law, 法 律 (houritsu). The character combines water (three dashes on left) with container and has connotations of watertight container. This notion was extended to mean restraint of human behavior and is also found for instance in the word for grammar, 文法 (bunpou).
(Rather nullifying the above line of thought, in Oriental Mythology p23-5, J.Campbell equates dhárma with Tao as a conception of how the universe works.

And as the Tao Te Ching has said of the tao, so say the Indians of dhárma: its yonder side is beyond definition; its hither side is the mother, support and bearer of all things.

*gere (PIE) - Crane (English)or in Irish An Corr

O.E. cran "large wading bird," common Germanic (O.S. krano, O.H.G. krano, Ger. Kranich,Welsh garan, Lith. garnys "heron, stork").
Although this bird has been absent from Ireland for about three centuries the birds role in ancient society has been forgotten. This is due in part due to the fact that its name in Irish is similar to that of the Grey Heron (An Corr vs An Corr Glas). The animal appears to have been domesticated and is thought to be represented by the bird leading the procession on the Ahenny Celtic Cross. Knocknagor (cnoc na gcorr - hill of the cranes/herons); Reaskcor (riasc corr - marsh where cranes gather);.

ताराtārā (SKT) - goddess of compassion

Taras are goddessess of compassion that are each said to be a personification of a tear of divine compassion. There are references of up to twenty one different taras who are differentiated, in the first instance, by colour. ie. the White Tara, Green Tara etc. It may be noteworthy that in James Joyce's Finnegans Wake, Isabel falls to earth as a singult tear and the names of her twenty eight companions are all colours.
The Sanskrit title has two meanings: saviour and star. In the first sense it derives from the Sanskrit root tr?, which means to cross, traverse (river etc) to transport, surpass or overcome; also to liberate and to escape. In the latin noun ter-minus, boundary, limit, terminal, term the emphasis is shifted, the Roman deity Terminus, presided over boundaries.
The second sense, star, is derived from the Sanskrit root, str?, which means to scatter, expand or spread out and is related to the English star, aster and strew.

माया māyā (SKT) - the world illusion

The Indian term for illusion is māyā derived from the Sanskrit verbal root to measure, to measure out, to form, to create, exhibit or display. It refers to the power that creates an illusion and the illusion itself. Māyā is experienced as fascination, charm; specifically feminine charm. It is said to possess three powers: a Veiling Power, a Projecting Power and a Revealing Power. Related to the PIE root for moon?