Hi can i use my logitech keyboard,mouse

Yes.

You don't have to use an Apple keyboard or mouse, the original Mac Mini was a lowcost computer designed for Windows users who wanted to keep their existing accessorties.

However, newer feaures such as finger swipes do require an Apple trackpad or Mouse.

Many - if not all - of them will work just fine

http://www.apple.com/uk/macmini/features.html#peripherals

Your 4 year old wireless n router will work.