Below in bold are my answers to your questions, mind you this is how I do it and not the only way to do it.
When I receive my rent checks, how does the cash flow get to my personal bank account, where I have freedom to spend it?
You can write a check to yourself from the business account that you set up.
Should I set up another checking and saving account specifically for this rental? I do not have an LLC so this would still be a personal bank account. should it be through a separate bank, or my personal bank?
Come up with a name for your business (Kingslien Rentals for example). Then you file with your state for a fictitious name (DBA, or Doing Business As). This is easily done with a form you download from here. The cost is $15. Once you have that you can get a EIN (Employer Identification Number) from here. They are free and instantaneous. Once you have those two documents you can go to any bank and open a checking and savings account in the name of Kingslien Rentals. The checking will be for rent checks and all expenses and the savings account will be for security deposits.
If it do set up a separate account for this property, can I have the mortgage payment directly drawn from this account?
See above, and the mortgage payment is a business expense and should come from the business checking account.
What do I do when tax time comes, and will they define my taxable income differently that what I have determined my cash flow to be?
Yes, it will be different. Most of the expenses will transfer over verbatim but most specifically any loan pay down will be considered income and not an expense, so only the interest portion of your mortgage payment will be considered an expense by the IRS. It is imperative that you speak with an accountant ASAP so that you are on the same page. It will cost a little bit now but will save you come tax time.
Where do I keep the security deposit and repair funds?
Although not legal required security deposits should be held in their own savings account. In Wisconsin they do not need to be held in a trust and you are not required to pay the tenant interest. If you wish to save for repairs outside of your checking account then set up a separate savings account for that purpose.
Should I open up a new checking and savings account with each new property (this seems like it would be very hard to keep track of all these different accounts).
You can, but I do not. I use quickbooks for everything and keep each property separate using the "class" feature. This way I can use one account for all rentals but I can still generate reports for each individual property.
How do I pay myself?
Write a check or make a withdraw from the Kingslien Rentals checking account.
Should I pay myself monthly, or yearly?
That's entirely up to you. You can pay yourself daily if you wish.
When I do form an LLC, how will all this change, and is it more complicated?
Honestly if you set it up as outlined above nothing will be different when you form an LLC.
All of this being said I highly recommend getting quickbooks to track everything. Operate the business as if it were it's own entity, track everything and enter it into quickbooks. If you have any other questions just ask.
