Can You Get Ultra Rare Skins in Hextech? (Black Alistar, Urfwick, PAX, etc)

No you can't, the skins that you list are limited skins and cannot be unlocked.

Legacy skins however can be unlocked since they come out of the vault every now and again anyways.

This page has more info: https://support.riotgames.com/hc/en-us/articles/201752944-Guide-to-Legacy-and-Limited-Skins

Pretty sure, yeah.

I got a legacy skin (workshop nunu) so idk if that counts.

If you can get it in a mystery box, you can get it from Hextech. (So to answer you specific examples: no, you can't get those)

yes u can get them cuz u can get all skins in hextech, even the ultrarare

You can get Legacy skins, such as Unmasked Kayle, Hextech Sion, Professor Ryze - http://leagueoflegends.wikia.com/wiki/Champion_skin/Retired_skins

But you cannot get limited access skins like PAX TF, human ryze and seasonal rewards.