You absolutely should have a separate banking account, and should keep all transactions related to the business separate from any personal transactions. If you are the only owner of the LLC this isn't as essential as it would be if there were more than one owner, or if you had incorporated, since the LLC structure essentially allows you to pay the business taxes on your individual tax return. But you will want to be able to separete the business income and expenses from your own come tax time, and the $15 a month or so for a busiess checking account will be worthwhile.
Then, yes, you can write a check for yourself. But I wouldn't see any reason to treat yourself as an employee and add that extra layer of taxation -- that would defeat the purpose of an LLC. The check you write from the business to your personal account would simply be profit of the business. You're just moving it between accounts, in the end it will all be the same on your tax return. Again, this is true if you are a single-person LLC. IF there are other owners it gets messier.
But really you are getting into some complicated tax issues, and should talk to an accountant about your particular situation. It's really worth spending a couple hundred dollars a year for professional advice (assuming you are making enough profit that the idea of paying yourself even comes into play!)
By the way, if you are an LLC (or a corporation) you don't need to register a "fictitious name" or DBA, unless the name you want to use is not the name of the company. To open a business account you'll need whatever certification you received from your state regarding formation of the company.