Money you can get anywhere. Coin purses laying around, single coins scattered around places. You can even sell equipment, weapons, books, and anything else you find on your travels. Most of the larger towns and cities, such as Whiterun, Riften and Solitude have shops you can sell stuff in, and the type of shop will determine how much you can get for each item. You can identify shops by the hanging signs outside. These are only open during the day and attempting to enter them at night will count as trespassing. If you come across a bar, chances are they'll have a room to "rent" for about 10 coins, though this depends on the settlement. These are also identified by the sign outside the building.
Usually if you get arrested, you have the choice of paying the fine, which is dependent on your bounty level. If you've stolen a small item, you should only have to pay a small fine up to what the item is actually worth.
You won't come across dragons too much, for the time being. I only recently got attacked by my first random dragon, and I'm at level 14, roughly. You're more likely to find them guarding word walls, which are important if you're wanting to learn all the different Shouts. Some of these dragons are easily defeated with a strong enough weapon. I'm trying to find information on what part of the main questline they start appearing with more and more regularity.
Lastly, have you changed your control layout to legacy, yet? You should either be able to do this ingame through the options, or your defaults throught the XB360 dashboard. Knowing the difficulty you have with the normal control layout, I strongly recommend you change to Legacy before you go any further.
If I have left anything out, let me know.