Is this tire properly fitted on the rim?
I'll answer all your questions in order.

1) "Will this tire wobble wear down the bearings faster, or other components?"
   -Nope, this wobble will do pretty much nothing to the rim. If anything, you will feel the slightest of 'floating' (the only way I can describe it, the bulge ever-so-slightly lifting the bike when you go over it.) 

2) "is this amount considered normal, and won't do any harm?"
   -Any tyre wobble is not classed as normal, though it will not do any harm to you, the bicycle or your bike's performance.

3) "Is this as true as you can get on such a cheap bicycle?"
 - The bicycle has nothing to do with the tyre. If the bike was £120, you can still get £80 Continentals. The tyre's quality, however, is quite a big factor. If you bought them for £12 a piece, there's a high chance that there may be minor defects.

4) "Should I spend more time trying to adjust or leave it as it is?"
   -Leave it. If anything, you risk doing more damage to the tyre/rim, constantly playing with it.

Ride around on this tyre for a couple days. In my experience with cheaper tyres, they'll settle down. It's usually due to storage/transit. Re-inflating usually gets rid of any deformation, though not always. Riding it for a while will eventually get it to even out.

If the tyre is damaged, you'll usually notice a very major bulge. If you take an innertube and inflate it, looking at the valve, you'll notice it has a weird shape around where the valve is. It'll look somewhat like that, but on the tyre.