I’m assuming this publisher doesn’t want money from you - either upfront or in the form of an expectation that you’ll buy copies of your own book. If it does, run away. Vanity publishing can be what some people want, but I don’t get the sense it’s what you’re after.
If they don’t expect you to send them money - ever, for any reason - then check out what they’ve done for their current authors. Check their Amazon rankings; if you have contact with any of them, ask how their sales are - ranges rather than figures, if they’re not comfortable discussing figures. You say you want a readership and a couple of thousand bucks per book (and the two usually go together): has this press achieved that for their current authors? If not, what makes you think they’re capable of achieving it for you?
Also, what exactly are they contributing? Do you have solid reasons to believe it’s worth their share of the take? Like, I assume they do the editing: have you read some of their books, and was the editing good? They do cover art: how’s the cover art on their other books?
What on earth could be wrong with this? If you want to make a career out of writing, then an agent is an excellent idea. If your current book isn’t good enough to snag one, write another one that is. Writing is like any other skill: it takes work and practice - if your first or second or third effort doesn’t take the world by storm, there’s nothing surprising about that, and it doesn’t mean your fourth or fifth can’t be the world-stormer. (And again, never EVER give an agent money. Never. No matter what.)
Depends on the publisher. Some niche ebook publishers (I think it’s mainly romance and erotica, but e-publishing isn’t an area I know a lot about, so don’t take my word for it) have a strong following of people who do buy from their websites. Again, check with their existing authors about sales.
Hell no, it’s not. Professional publishing companies don’t know or care what their authors think of the contract. They’re busy publishing and marketing books, not getting into internet bitch-fights. A publisher dropping authors who dare to criticise the contract is not a good sign.
I’d check out the publishing house at www.absolutewrite.com. They have a good background-check board.