Taken in order...
1) No. There aren't markets which make allowances for new writers. Even the contest markets (Writers of the Future, Strange New Worlds, etc.) are looking for professional quality work from new writers.
I don't think it would be healthy if there were. As I have said before, publishing may be a meritocracy, but it's not a just meritocracy. Story trumps. New writers have new voices, new visions. What good would a market do that was deliberately seeking to buy less than the best stories which present themselves in a slush pile? How would you react as reader to something like this?
You don't have to be a Name to write a good story. You don't even have to be experienced to write a good story. You just have to write a good story. How to get to that point is a complicated and sometimes controversial process. It's a tough world, a tough market, and near-psychotic persistence counts for a hell of a lot.
(Lest anyone feel I am thoughtlessly dictating from my lofty perch as an established writer, please bear in mind that I wrote and submitted a very large amount of material for about 10 years before I had my first sale. I vividly recall the frustration of that process. What made me better wasn't the presence of an accomodating market or editor, it was the practice that a decade of idiot persistence gave me. pauljessup pretty much covers it here.)
2) Guidelines are made to be broken. Some are more elastic than others. A market will tell you in flashing bold letters they won't buy vampire kitten stories, ever, under any circumstances, but if you send in the best damned vampire kitten story on Earth, they might buy it. Then again, they might not. "Seen it before" plot warnings can be trumped for a good enough story. On the other hand, length restrictions may be hard-and-fast for unwaivable reasons of publishing economics. This requires a balance between honest assessment of your work and an understanding of the market in question. There is no easy rule of thumb. Either follow the guidelines or don't is what it boils down to.
Bear in mind there is a relationship between the degree of writerly trust you hold (depending on your career level and the editor's knowledge of your work) and editorial willingless to overlook guidelines. Gene Wolfe could send in stories written on butcher paper and draw very serious consideration, where you or I would be bounced for having an unreadable manuscript. As an established-but-newer writer, I can probably take more liberties with market theme and acceptable plots than an unknown aspiring writer. Again, it's not fair, but that's the way of the world. Also, again, story trumps all.
3) Editors don't remember bad stories. Unless you're writing heroically bad, "Eye of Argon" level stuff, they literally won't think of it again once they've rejected. (Or unless you do something bizarre, such as put the editor or their children directly into the story as characters. Don't do that, trust me.) They do, however, remember names. So your regular appearance in the slush pile with steadily improving work counts a great deal more to the good than a moment of the giggles over a howler in an off-the-mark manuscript will ever count against you.
It's also a truism that a writer is the worst judge of their own work. You don't know how good or bad a story is until you send it into the world. I'm not suggesting mailing out every piece of dreck that happens to roll off your keyboard. I am suggesting that trust yourself and your stories enough to mail the manuscripts out to the best markets for you. (For a discussion of what constitutes "best market", see the earlier post referenced above.) Don't worry about not being good enough. Bluntly, you probably aren't. I've never been good enough for F&SF, and I have well over 100 rejections to prove it. Still batting .000 with Gordon to this day. But the only way you or I can ever get good enough is to keep writing and sending.