Can any one tell How big VLS system is need in ships to fit this missile on them ?
Babur is the size of Tomahawk. Tomahawk only fits in the deepest MK41 cells.
Therefore, Babur would need a VLS of similar size.
Another option is to keep a system similar to the current Babur tel. Tomahawk used to be packed onto ships in armored box launchers, like were found on the reactivated Iowa class battleships.
They're pretty big, so as
@Oscar notes, space on the helipad would need to be allocated to fit such a launcher.
Since your ships are too small for the VLS farm of the Burkes or similar sized ships, a smaller 8 or 16 cell, like is found on the Nansen class frigates might be an option. Perhaps not right behind the gun, maybe somewhere on either side of the superstructure, but it's doable regardless.
Something like the MK48 Mod 0 which can be placed where there is space.
At sea i have no idea as the target will be moving.
They'd have to use a form of TERCOM called Automatic Target Recognition. Like TERCOM, the missile is loaded with the known profiles of ships and automatically ids, tracks and attacks the ship based on data it stores inside and matches. These profiles can be radar signatures, IR, electromagnetic, acoustic or any other profile type. It requires major processing power and for the missile and operating nation to know the signatures of the ships it's trying to attack, but it can id, track and target ships in real-time, where as TERCOM is most suited for targeting static targets like runways or bunkers
Modern missiles like LRASM and NSM use this type of guidance. GPS gets you to an area. ATR, IR or active radar homing get you to a specific ship.
Satellite cuing has been used for real-time targeting too. A2A engagements using satellite tracking and guidance of AIM-120 and AIM-9 have taken place as an augment to radar or IR guidance, which are easier to fool or jam then satellites.