Tossing this in, more or less in random order.
And I'm talking about standard mass market Romance genre.
-- unsympathetic heroine?
In Romance, the reader has to like the heroine.
That means snarky is okay. Malicious is not. Materialistic is okay. Greedy is not. Unsure and shy is okay. Cowardly is not. Jealous is okay. Cruel is not.
It's all in the shading.
-- Can the heroine kill?
Yes, if she has a good reason. Killing in defense of somebody else is particularly good reason. While it's not Romance, see Eve Dallas for a precise lesson on when and how killing is done. UF, (also not Romance,) does killer heroines a lot.
-- Can the heroine screw around?
Before the book begins, yes. Afterwards, no.
-- Can you kick the damn puppy? Speaking metaphorically.
Terrible things can happen in Romancelandia.
They are terrible things of two sorts.
There's the suspense/thriller/mystery/action kind of terrible thing where the heroine wades into the crash scene.
Romantic Suspense has a large audience. The book will be clearly marked as what it is.
But 'kicking the puppy' is something else. That's not the crash scene with anonymous dead, it's the heroine's little sister hit by a car. It's her child dying on-stage from leukemia.
That is rare. Possible, but rare.
-- Can you kick the puppy literally?
As to real puppies - -
Can you kill them and cut them up for stew meat and cook them for dinner?
You're going to lose readers right that minute the puppy squeals and dies. Books are going to snap closed.
Readers -- lots of them -- will not buy a book where a child is harmed. Where an animal is hurt. Where serious bad things happen. They check reviews to make sure nothing really bad happens.
-- Rape?
Rape of the, 'he raped me and now I love him' trope, is an automatic, 'put it back on the shelves' for most readers. I wouldn't call it forbidden, but you definitely limit both the editors who will find this acceptable and the reading audience.
The same titillation, without the act itself, will be more marketable.
Rape or being molested as a child, when it is a horrible, past trauma, is not uncommon.
-- Child haters?
The heroine not wanting children and not fond of children is okay.
Truly disliking them will probably come across as unsympathetic. I'd call it not utterly forbidden, but another thing that limits the readership.
-- Sexxing.
I will not begin to list the sexual acts people do not perform in Romance books, but they are many and varied. Also forbidden are most of the words used to describe these acts.
Simple intercourse occurs with great frequency and in some detail. There are some references to oral sex. So, not forbidden.
OTOH, masterbation is so rare I can only think of three or four instances in mainstream m/f Romance. I have no idea why this is off-limits.
-- Not wanting to get married
. . . and not ending up planning to get married.
Not forbidden. It's part of the HFN movement.
-- Serial books with the same protagonists.
Because Romance genre is 'courtship' stories, books that deal with the later development of a relationship tend to ease right over to the edge of Romance genre and out the side into General Fiction or Historial Fiction or some other fool thing.
That said, this serialization has been done again and again. It may get you moved to another shelf in the bookstore if you keep it up.
-- Multiple POVs
In shorter lengths, craft is going to keep you to two or at most three POVs, not some Romance rule. It's technically difficult to develop more than 2, or at most 3, POVs in 60K words.
Longer lengths you can play with more POVs. I think I've used five.
-- Exotic settings?
Exotic works for Contemporary and Historical, Category and Single Title. Nothing is forbidden.
BUT there are expected and familiar settings. If you venture outside the familiar, it'll be more difficult to sell.
-- the first male?
S&S makes an excellent point. The males introduced in the story have to be eliminated as heroes . . . unless they are the hero. They have to be too old, too young, too evil, of the wrong social class, related and so on.
It's sort of a Romance convention. Yes.
-- the providing male
The hero of a Romance is almost always desireable in terms of money, earning potential, power, and status.
In an era where many women out-earn their husbands, I don't see Romances where there's a presumption the woman will be providing economically for the man.
Maybe because I mostly read Historials.
I suspect this is not forbidden, but just seen as removing some of the glam from the HEA