1. [ɡilɛ̃] is definitely the expected¹ pronunciation of Guillain. This last name is certainly a variant of the (first) name Ghislain (Saint- Ghislain was at some point written Saint-Guillain). That can also be written Guislain also pronounced [ɡilɛ̃]. Unfortunately, the alternate (and incorrect) pronunciation [ʒislɛ̃] is spreading and by far the most common in France and Canada now. In any case, there is never a [j] in these pronunciations.
2. ..[vowel]+illa is as far as I know always pronounced with a [j] in French words, I can’t find a single exception. The proper names Fuilla and Quillan are also pronounced with a [j] as their Occitan/Catalan form show (Fullà/Quilhan).

Guillain is not really an exception because its u is not technically a vowel but only there to keep the hard [g] sound before an i. Otherwise g would be pronounced [ʒ].

Same goes with Guillard. There is no definitive rule for pronouncing the double l in “illa“/”illain” but a [j] is largely dominating. I would then expect either [gijaʁ] or [gɥijaʁ]. There are only few cases of [l] like villa, villages, chinchilla, capillaire, villain (modern spelling: vilain) and … arguably Guillain.

¹_{I write “expected” pronunciation because as Quentin Ruyant also commented, there is often no rule for proper names. Georges Guillain’s family might have decided that their name is to be pronounced some other way but IMHO [gijɛ̃] is more than improbable although the one often documented in English dictionaries.}

I am a french speaking Canadian. I have never heard anybody saying ʒislɛ̃ . There is a some question between gijɛ̃ and gilɛ̃. I’ve learned in university and in neurology formation the use of gijɛ̃ . Since Dr Georges Guillain was french and my french cousin “dda” up here confirms in France everybody uses gijɛ̃ , that ends the debate for me , thank you !!

What Dr. Guillain called himself would seem to be most important. See Pronunciation of Dr Georges Guillain’s name JAMA. 1977;237(23):2470