Hi Jenni, and welcome to Salehoo,
It's good to see that you do have a good grasp of the realities of Drop Shipping, that's actually a great start.
To respond to you questions,
1. Finding a niche market isn't that easy these days and can take a lot of research with plenty of test marketing to arrive in the right place. This is just a personal opinion, however I think it can often be a waste of time these days as so many are watching for emerging markets by way of various research tools, ours included.
These tools make it easy for others to keep a very careful eye on what is selling and they can help id a niche that someone else has done all the ground work digging up, and then jump on it. As you can imagine, it doesn't take too long for everyone to jump on and your niche turns into a heavily saturated market over night.
OK, so that's all a little dark and gloomy, and to balance that, some do find a niche and service it well. I think the big secret these days with a niche market is to find one that just has a nice steady turnover, not one where demand outstrips supply too radically, because those are the markets that can go off with a bang and draw everyone's attention to them.
Under the radar as much as possible, and I would suggest that if you do find a niche market that you move to setting up your own online store to develop the market further. You can use your site to then really develop the niche, while staying under the radar on eBay and still use it as an effective sales funnel.
2. In regards to fixing prices, yes you can fix prices on eBay without having a store, and I recommend you do exactly that. When setting the price, ensure you are covering all the avenues, item price, PayPal fee, eBay fees, both listing and final success fee and any other associated fees.
This is actually a good little research tool itself. Once you know how much you need to charge just to cover yourself, then you can research eBay to see if there is any margin left for you to make money against other sellers.
Good luck with it all :)