It doesn't have to be 10 different dropshippers, it can be one or it can be as many as you like. I just suggest starting with 10 products to give yourself a decent chance, without getting burnt on listing fees. The most important thing is that you research the products on eBay or wherever you list them. You still have to make sure you are competitive with your choices.
Page Hit = How may times your page gets viewed
Watch Count = How many people put your item on their watch list
Sell Through Rate = How well your item sells per times listed
For example, if you list a product 10 times and get five sales, then you have a 50% sell through rate. It's a way to measure how popular your products are. High sell through rate usually indicates you're doing something right, slow sell through rate usually indicates your business needs fine tuning in some areas.
These are mostly relevant to eBay, but other sites may also have these types of tools to help you manage your business. In regards to listing on other sites, no effect to eBay feedback whatsoever, they aren't interlinked at all.
A high feedback score with good ratings is always a plus, but everyone has to start somewhere and a feedback score of 8 is fine, so long as you have a high satisfaction rating.
In regards to that supplier, that is a very high proportion of out of stock items. I'll get our support team to check that out and see if we can find out why they are running like that for you.
In regards to time zone, I'm not quite sure to be honest, but I would suggest calling after 1pm your time. If that doesn't work I'll get you to PM me your number and I'll have someone call you to assist.