even with maximum sneak, I'm having a hard time picking locks and remaining unseen, even when nobody is facing me. Any successful thieves out there with some tips for a newbie?

I didn't bother investing in the sneaking skill; my solution was to break in when there is nobody around. City streets are a lot less crowded at night, and some areas are completely empty even during the day. This is much more difficult in villages, but still not impossible.
Another thing to look out for during the day is buildings where NPCs constantly go in and out. As soon as someone goes in they unlock the door and it stays unlocked (at least until you leave the area or something), and since they only stay for a few moments before leaving (unless it is night) you can simply go inside and wait until they leave; time pauses when you have a container open, so even though someone else is probably coming along any moment now you can take your time deciding what to steal. One thing to watch out for when doing this is houses where people are in another room or upstairs (they will automatically know you are stealing, unless you pass the skill check I guess).
Another thing to pay attention to is houses occupied by quest NPCs. Many will be removed from the game once their quest role is finished--although you will have to leave the area and come back for this to take effect--and after this you're free to loot their now-vacant house (which will always be unlocked because it's meant to be easily entered to do the quest).

The penalty for being caught stealing seems to be pretty minor. I was in the house Skeldon and decided to pick open the improved lock chest while Ebrat Skeldon was sitting right beside it. It was a lucrative heist, and the only repercussion was Ebrat took a few swings at me, which I avoided and ran out of the building.
I came back 30 seconds later, and it was as if nothing happened. My standing with the faction wasn't reduced, and Ebrat would speak with me about quests and wasn't angry in the slightest.
This is my first foray into thieving in this game and I'm level 20. Is it always like this?

In towns with guards the guards will accost you and ask you to pay a fine of several thousand gold (if you can't/won't pay they will kick you out of the town forever, locking the gates to you if it has gates); in minor villages and other locations there are no real consequences, however.

When I tried doing that it didn't work (he took it as an insult and attacked me). I'm not sure what skill check this is based off--or if some guards can be bribed and others can't--but it's certainly not a guaranteed escape route.

The one I got to bribe was in the Excavations/Skeldon area. When I chose the option he complained about how poorly he was being paid there and accepted 10% (100 gold).
I like some of the dialog your character delivers. It's not always your typical goody-two-shoes comments you get from other RPGs.
Guard: "You plan on starting trouble around here?"
You: "Nay, too many guards around!"

I can't remember the towns name but I accidentally picked a doors lock. A guard came up and demanded $30,000, so I tried to do the 10% option. The guard didn't accept and attacked me
...
that poor town, every person brutally slaughtered because of that guards lack of greed :D