First, I am a little over 8 weeks and still have some bruising on my knee. I didn't think to ask the surgeon, but I am wondering how long it should take for it to go away.
I'm not sure that there is a set time, by which bruising should have gone away. Usually, it just fades gradually. As long as you're not niticing fresh bruising, just watch itg for a while and see what happens. Let your surgeon know if you have fresh bruising.
After my last TKR, I found that I had a residue of brown staining of the skin on some parts of my knee. My surgeon told me that it was iron staining, from the haemoglobin in the blood that had initially shown as bruising. It did fade eventually, but it took about 6 months to do so.
Also, I am having some pain in my lower back and hip when I am up and walking much at all. I am wondering if new shoes would help. My gait is good, but one leg is now straight and the other is not. Should I get new shoes now, or wait until after the other knee is done in January?
You will have had a change in your gait, since one leg is now straight. Getting used to that different gait does put a strain on your hips and your back as well as your knees, hence the pain you're feeling.
Ideally, you should get new shoes, because the pattern of wear in the old shoes will be different from the pattern you are making now - the angle at which your foot touches the floor now can be quite different. I can understand your reluctance to buy new shoe snow, knowing you'd probably need to do that again after January.
Have a look at the soles of the shoes you want to wear now and see how much of a tread pattern they have worn (it often shows more in the heel). If it's very noticeable, then you do need to buy at least one new pair. However, I'd try to make do with just that one, new pair, and wait until after your second knee is fixed before spending up large.