Every miner can only confirm transactions. Acceleration just means that they will give priority to your transaction in the next block they mine which for big miners is every couple of hours.
I am unfamiliar with "Windows Bitcoin Miner" and most are just malware. You can't just download a miner anymore, you need to buy special hardware in order to do any Bitcoin mining. I would suggest that you reinstall your OS as your computer is probably infected with malware (then again which PC that is running Windows isn't ? ).
As I said, one guy accelerated my transaction, as he said (I can't check it out, what exactly happened with my transaction). But what I see that it is still unconfirmed. So he said he gave prio to my transaction. Why do you say that every miner can only confirm? Direct after that you explain about an acceleration. But it is not the same as confirmation, isn't it?
So if I buy special hardware, can I at least confirm my own transaction, and I mean confirm not simply accelerate? (I read that profitability of the mining is very unpredictable, that's why I written 'at least'). What are minimal requirements for this hardware? Does this hardware contain all needed software as well?
(I have a Norton Antivirus. E.g. MinerGate Software was as malware identified and removed. But on Windows Miner, it didn't react.)
First of all, antiviruses are good at stopping wide spread well known infections. They are horrible at actually detecting viruses that are somewhat new, not wide spread yet or are staying dormant for a while. Don't expect from an antivirus to protect you, especially if you are downloading unpopular software from the Internet.
Secondly, it is definitely a virus since there is nothing else that it can be. It is not an actual miner, as I said, you need special hardware called ASICs for mining Bitcoin. I heard of these things many times, these viruses are common in the cryptoworld, they often pose as a wallet or for even more naive, as a miner or some kind of Bitcoin generator or even hacking tool for hacking Bitcoin. Or whatever a newbie will believe that makes absolutely no sense at all if you have any grasp of how Bitcoin actually works.
Acceleration is not a technical term, confirmation is. Acceleration is no specific operation, confirmation is.
Acceleration is just a term people use to say "your transaction will be confirmed faster then it usually would, since I will confirm it even tho I usually wouldn't because of it's low fee". So asking for a program to accelerate makes no sense, neither does your Windows Bitcoin Miner.