https://pushtx.btc.comHow exactly this work mean client buy push for one confirmation only?
Mean if exchange require 3, what then?
Once it will be paid and confirmed others start confirm quicker?
Am I thinking good? I mean not need to buy X times.
Transcatino accelerators like that one is only useful if you have paid less fee than the recommended amount for your transaction. If you've already paid a decent amount of fee then waiting a few hours would result in a confirmation anyways.
These services are basically mining pools that will selectively inclued your transaction in the blocks that they mine.
However, keep in mind that they are incredibly expensive to use and your first option is to always send the transaction with a high fee. So it's sort of only supposed to be used in emergency scenarios. There are also free ones like antpool.