In regards to Terapeak, I would suggest you use the SaleHoo Research Labs tool before even considering Terapeak. You'll find the Research Lab link in the red title bat above.
To tick off your other questions.
Whether you get a store will usually revolve around the volume of stock you list. Not much stock, no need for a store whatsoever.
No need for a business checking account, unless you want to use it to pay suppliers course.
A Tax id will be required if you purchase through wholesalers, but not for drop shippers or liquidators.
Yes, you can use the same PayPal account for multiple eBay accounts.
Yes, you can sell a broad selection of items from the single site if you want, in fact from a cross marketing stand point, it's the best option. Cross marketing is what shopping centres are based on, each shop get's the advantage of other shop's customers walking past their front door.
This is in fact where I would suggest a store as being the best option, and the then the trick is to set your store out well.
Define your categories and sub categories well, make it as easy for the customer to navigate as possible. Use listings to market other products from other genres, just because someone buys a ring, it doesn't mean that they won't also buy a hand bag or at least know someone they can point in your direction.
That's the whole idea of cross marketing. Sure, marketing products similar is talking to your immediate audience, but always leave plenty of crumbs to lead people in other directions as well or your not maximising your marketing efforts.
In regards to making your listings professional, I would suggest getting a template developed to give your store a uniform image. The essentials of the template should always remain the same, but you can change it up a little to define between product ranges.
For example, if you walk into a massive store, something like a big hardware warehouse. You will find the store remains the same essential layout, no matter what part you are in, but they may have different sections with different colours to define areas.
Building a professional online store uses the same techniques as building a professional offline store, so just think how you would layout your items if you had floor space to display. Think how you would define areas and so on, then take those ideas into your online store.