Centipede lawn care

I have a few questions about caring for Centipede grass. I cleared about 2.5 acres on my property, and laid centipede sod on about 1 acre. I heard Centipede grass seeds more than any other grass causing it take over most other grasses. (I hope I said that correctly) Well the second acre is starting to take on the centipede but very slowly over the course of 2 years. There is just this fine thin grass on the remaining lawn that wasn't sodded. I fertilized the grass with some stuff at tractor supply by picking something the rep there suggested.

The few questions I have is what is the best winterize to use now? I hear 5-10-31. Is this right? If so best place to buy it.

Is there something cheaper I can use like LimeLawn?

What should I fertilize it with and what time of the year?

If I fertilize it and keep it healthy will it spread more seeds per year?

Do I need to put any kind of weed killer in it? I hear a health lawn will drown out all the weeds and stickers.

I'm sorry I was long winded, however, everyone I ever talk to about it says something different. I live around the BR area if that makes a difference. I don't mind buying off line if there is a place online to visit also.

thanks in advance.
tigerweb