This depends on a lot of things.
The idea of preheating is that you want to get all the surfaces inside your oven (walls, floor, door, racks) up to the desired cooking temperature. This makes for more even temperatures throughout the oven, and gives a little thermal mass so you don't lose ALL your heat when you open the door for a few seconds or put something cold in there.
Then there's the question of what you're putting in the oven. An aluminum sheet with a few room temperature cookies on it won't pull the temperature in the oven down like a 25 pound turkey that's 40F/5C inside. You want to be more careful to do a complete preheat if you're going to be soaking up a lot of your starting heat.
Our oven, which has a large baking stone in the bottom all the time, takes a while to get uniformly up to temperature, even after the oven says it's preheated, because the stone doesn't heat up as fast as the rest of the surfaces. It takes at least 20 minutes after the "I'm fully heated" beep before the stone is fully up to temp. We have problems with things baking poorly if we don't preheat for quite a while, but on the upside, if we put a cold roast in or open the door a lot, the temperature in the oven stays pretty high.
If your oven is lightweight, flimsy or drafty, it may be as hot as it's going to get the moment the preheat alert goes off.
45 minutes is probably a lot more preheat than you'll need in almost any case. In some cases even 15 minutes is more than you need. It really depends on your oven and what you're putting in.
It sounds like the oven needs desperately to be looked at. Please have someone check it out before a fire starts!!!!
The thermometer placement isn't a huge concern. It should be near the middle for general use (top to bottom) and off to the side. Or if you prefer you can just hang the thing in the middle. As long as you can always safely see it it should be fine. If your coils are on the side and not top and bottom put it in the center (where the window would normally be)
Really though I can't stress it enough. If your setting it to 350 and sometimes it is temperature x and sometimes it is temperature x + 100 then you really need to have it looked at before it gets worse.
Best Answer
First off, try and check the temperature more carefully. By far the most common reason people have trouble with their oven is that the temperature isn't what they think it is, and burning is a really good sign of that. It's very likely that when you set your oven to 350°F, it's actually hotter than that.
Ideally, you should check the temperature the bread is actually experiencing: put your oven thermometer next to bread while baking it (or an empty bread pan in that same position). The pan can disrupt the air flow, so the temperature the bread experiences might not be quite the same as the temperature in an empty oven set to the same temperature. You should also check more than once, in case it's just unreliable.
And yes, smaller ovens can exacerbate this. Baking sheets/pans will take up more of the oven, so they'll disrupt air flow more. The other thing that can happen in small ovens is getting too close to the top or bottom of the oven, so that the edges burn even if the temperature in the middle is okay.
If none of that is an issue, then I'd look elsewhere: