If they aren't even selling books, but giving them away for free, then run away. How do you expect to get royalties if you don't actually sell the book for money?
While it's absolutely the choice of the self published author to put a book up for free (and I know it can be a great marketing tool), this is not something a legit publisher would do. How in the world would they recoup their investment? Who is paying the illustrator? The editor? The formatter? The marketing team?
They are not acting like a legit publisher, just to let you know. We as authors don't get to decide a) how many books to publish or b) when to publish them. There are publishing seasons and certain books do better at certain times, which is why release dates can be important and are often planned YEARS in advance. You are indeed right, a legit publisher focuses on the first book in a series first. While it wouldn't be out of the norm for them to request a brief outline or synopsis of the second book, the focus should be the book that is actually written and ready for editing. Also, as far as I know, while the publisher does have final say over the illustrator typically (depending on the contract), usually they take the author's input into consideration and often offer several options. Or at least that's been the experience I've heard of from my friends who have published PB.
Badly run presses and scam agents are becoming a problem with Twitter Pitch Events. Small presses have taken notice of all the people pitching and try to get their piece of it. And while some of those presses are totally legit and great, not all of them are. It's very frustrating and you are smart to carefully research anyone who approaches you through something like this.
Personally, this is not something I'd be willing to pursue. There are way too many red flags already and they just emailed you this morning. If you do decide to get a contract sent to you, you'd be best served by hiring a lawyer to look over it for you. Don't sign anything unless you have a lawyer, because you may be signing away rights that you don't want to give away. I'd also ask them who is running their press and what publishing experience they have. If they have none, or dodge your question, RUN.
A publisher who gives away their books instead of selling them, who has errors on their web page, who doesn't act like most presses do, and who is very new is likely not a good choice for anyone. I'd focus on PB agents if you want to go the traditional route and consider this a bullet dodged, in all honesty. Remember that anyone can put together a web site and call themselves a publisher. Actually having the experience and connections to make a small press work is much harder. It doesn't sound like these people have those things. They may have great intentions, but the reality of publishing requires much more than good intentions.
