I don't know if she can train up to level 100, but one of my goals has been to pay her goodness knows how much for those last few levels, (I'm at 92 or something), and then immediately pickpocket the money straight back off her. However, it always shows as 0% chance to steal for me. But you're right, she's had about 10,000 gold off me. And she still wanders around in those rags, thanking my generosity when I give her 1 gold and increase her fortune by 0.01%!!

Not really related to helping beggers but more along the lines of the feeling of 'helping' and having an impact I find there are too many NPC's in this game called generic names, like 'Farmer' or 'Traveller' I would have prefered to see more named NPC'S. Beggers in Oblivion made more sense to me cause they actually seemed to have a routine and had beds (never seen a begger sleep in Skyrim, may be wrong though)

Can you reverse pickpocket them some clothes to wear? I'm just asking because I haven't tried it myself. Or would it mess up their beggar look and keep them from getting charity from others? I kind of with there was an intimidation option so you can punk them for their change.

On your way to the Cloud District, obviously.

You cannot help those who won't help themselves.....the poor will always be with you....

They want mead bro! I always give the beggars a septim so they can forget their problems for 5 minutes or so