Water getting in under window frame.

This is an old terrace house bay window, lots of damp and mould growing on inside so ive hacked away around the bottom of window to see where water is getting in.

Seems to be coming in between the stone sill and window frame.

So 2 questions.

1. Should i caulk under the window on the outside, or is this bad due to blocking vents?

2. How should i finish the insode reveals? Caulk bottom of window first, then fill in with ready made plaster or cement mix? Expanding foam and upvc sill?