Ooooo yes please.

1. Unless her situation direly calls for it, Elayna would rather rely on her own skill than that of an enchanted item, because items can be lost or broken. Learned skills can never be taken from you. So, even if it's seemingly made just for her, enhancing alchemy or magic, she'd be fine with returning the item. However, she would ask for proof, family stories or the history of the item before she handed it over. If the supposed owners are in fact lying, then she most likely would sell it. Quality reagents are expensive, after all.

2. Elayna would turn around right then and there. Money isn't so important to her that she'd stoop to harming children, no matter how brainwashed. If she were to employ some method of administering sleep or paralysis poisons, then maybe she'd not be so disturbed, but that would imply slicing the kids with her dagger or hitting them with a dart (Hm...are blowguns even a thing? Maybe in Akavir or something...NOW I'M CURIOUS). Even then, she would be out of poisons to deal with the chief by the time she got to him. Big chief with large sword versus tiny alchemist with a dagger and ice magic could be bad if she's already worn out. In short, she'd drop the job as soon as she knew, even though it'd mean leaving criminals running about. Someone with more of a stomach will hopefully pick up the job.

3. Living in the Imperial City, she has had to deal with drunk noblemen looking for a hook-up in the taverns several times. With those, she normally just popped back home, cooked up something terrible (say, something akin to slightly diluted Ipecac), and the next night, if they showed their face again and happened to keep up the same act, she'd use her womanly charms to get close enough to spike the drink (tell them it's a very rare brew from some province or another) and scuttle on out of there before the fun began. Same would apply here. Elayna does not like drunkards at all, so she's not above a slow and methodical (non-lethal) revenge to teach them a lesson.

4. This is something she'd have dealt with on a daily basis. If she noticed a chronic beggar, she would try to get them on their feet, maybe going around and using her connections in the city (a perfume saleswoman and a medicinal alchemist tends to be popular with a few of the city breadwinners) to try and find him work. If that doesn't work out, then she would give him a few Septims, food, and a vial or two of medicine that she made (can't rightfully give her own store's stock away) to tide him over, if she was sure he truly needed it and simply wasn't extorting the public. Elayna wouldn't lie just so people can be comfortable or less annoyed, especially if it took a man's freedom.

(P.S. working on a little something with Nyx)