You're asking a lot of questions at a time that's not good to start changing your mind or to re-shop a product. First, you should feel free to challenge the installer with the questions you pose here. With any luck, the help I give and anyone else gives you between now and tomorrow (install day), may be of good use to you. Unless your installer is willing to do last-minute changes in his plan, you may be stuck with what he has planned. If it's possible, see if he (and you) can post-pone the install. You may not want to tell him you need more time to do some 'homework' though. I'll leave this up to you. In the meantime ...
Most stain and finish products are driven by personal preference. Although some products tout that they do more than others, unless you're staining something that's gonna be exposed to the elements, most interior products are relatively the same. When it comes to exterior or underwater products, you can't compare. (Moving right along ...) You should shop the labels and talk to folks to see how well different stains and finishes held up to their expectations. Most stains today come with a sealer in them. The Application Instructions will say if you should seal the wood first, or not. (If the label says NO and you seal the wood anyway, the stain won't get absorbed.) My preference for flooring is to get a stain that seals the wood at the same time. Remember, the darker the stain is to begin with, it will only get darker over time. So I suggest you go as light as possible a stain as you can tolerate. As far as Bennette is concerned, if you aren't comfortable with it, don't use it. Do understand that just because their paint products seem inferior, that doesn't automatically translate into their stain & finishing products being inferior too. I would recommend a water-based finish for a floor because it lays better with multiple applications, dries quick, cleans up quick, and doesn't smell like oil-based finishes. Bennette did make their name with paints so it's up to you.
Varathane is a decent product. They make good marine varnishes and stains too. If he/you want a moisture-cure product, Varathane is a good way to go. And 'superior' branding is a lot of hype. Personally, I'd go with the Varathane.
Hope this helps. You don't have much time to react unless you can have the install postponed to catch your breath. Best to ya.