I'm no lawyer but I do have an LLC in the state of Utah for each of my real estate ventures. I do not have rental properties (yet) but when I do, I will put each home/unit under their own LLC for the liability protection alone. If something were to happen at one of my rental properties and a tenant attempts legal action, they can only sue for the max value of that particular LLC (or property) and not my entire portfolio (is how I understand it). Luckily I have not had any legal action on any of my LLCs so I haven't tested this.
There are still self employment taxes when you have an LLC and that's why I actually have an S corp that owns each LLC that I own. This rids myself of self employment taxes because it treats me as an employee of the S corp. I just pay myself a nominal salary and the rest of the earnings are disbursed as dividends to the stockholders (me).
To answer your last question, I believe you do have to pay taxes in each state. You will have one federal tax return and one tax return for each state that you earned income for that tax year.
Again, I am no lawyer or CPA, so I recommend consulting with professionals that actually know what they are talking about.
Good luck!