Followers are generally given a set of skills that will improve, regardless of what you equip them with. These will improve with level, but nothing else will. Faendal is always going to do better with bows than with a greatsword, for example.
To this end, the official strategy guide states:
- Sven's skills are alchemy, enchanting, smithing, and archery
- Lydia's skills are in one-handed, heavy armor, archery, and block; not sneak
It's not clear where the rumor that Lydia would make an excellent thief started: UESP mentions she has the sneak skill on the list of followers (I suspect that's where Wikia pulled the information), but her wiki page clearly marks her as a warrior (the correct designation). Nothing about her says "stealthy": she starts with a sword and board and tells you over and over that she's there to protect you.
While the official strategy guide does list what each follower's skill is, with the exception of Lydia, UESP's version matches up with the strategy guide, so it should be pretty accurate to determine what skills your follower has.
But if you wanted to do it without consulting a guide or a wiki, it's generally common sense and usually based on what equipment they come with. Lydia comes with a sword and shield, so her skills are one-handed and block; Faedrun comes with a bow, so one of his skills is archery; and so on.
I loaded Lydia up with some Iron Ingots and Leather Strips, enough to make several different types of item. Then I commanded her to use the forge. I didn't get a crafting menu or any means of commanding her to craft a specific item.
She used the forge for a while (carried out all the various crafting animations), I left her at it for five minutes realtime and checked her inventory. She still had all the ingots and leather strips I gave her, and she hadn't crafted any items, despite having appeared to have been crafting for a long time.
So at least for Lydia it seems that it's not possible to craft items.
Best Answer
Yes. See which followers specialize in casting spells in the UESP wiki's "Followers" article.
There is no need to do this for followers that can cast spells. These followers will automatically cast spells in combat. However, when given staffs, followers (even non-spell casting ones) can cast the spells of those staffs*, provided those staffs are charged with souls. In a way, you can manipulate a follower's inventory to have them cast spells.
*Related question: Which staffs will be used by followers, when given to them?