If you buy a new sniper then again do you have to buy the silencer?

You have to buy a new silencer for each different sniper rifle you buy - you can't transfer it between different sniper rifles.

Many players don't waste their diamonds on silencers (it costs 14,000 diamonds for silencers for the higher tier guns); one advantage is that nearby players won't hear you shooting in PVP games (and therefore not turn around and shoot you straight away), but some players who have bought silencers say it has affected their feel for the game by not being able to hear themselves shoot their weapon.

You will end up spending/wasting many diamonds if you want silencers - the diamonds would probably be better spent on other parts of the game, such as (i) helping you getting through the PVP Arena Challenge (ii) when first buying tactical gear so you survive for longer in the PVP battles, or (iii) hopefully on some permanent mods to help you get through the World Ops levels faster.