Inter satellite links are basically fiber, just without the fiber (instead they just point the laser in the right direction and rely on the fact that space is empty). Up and down has to use valuable radio spectrum, handle interference and atmospheric effects, etc.
Nope, all v1.5 sats have them, so everything launched since January 2021. They experimented with them earlier for polar orbit sats. At this point that's by far the majority of the constellation and either approaching or at critical mass for the mesh. They're probably testing it globally now.
To sibling: they definitely need Starship, but not so much for pure launch numbers as the ability to launch v2.0 at all. F9 fairing isn't big enough. 2.0 will let them shrink cell sizes and improve density and performance which they need too (obviously now more in light of yesterday's announcement). More 1.5 sats wouldn't help as much with that, though the mesh will help relieve ground station chokes as well as ilenabling beyond station service.
Right now Starlink is a bent pipe model. The customer's station connects to a satellite which relays data to the closest ground station. Therefore, the satellite must be in contact with both the customer station and a ground station at the same time. This is not possible over oceans.
Newer Starlink satellites also have a satellite to satellite laser link which is intended to allow relay from consumer station -> satellite -> other satellite -> ground station to provide coverage over oceans, but this functionality has not yet been enabled and relies on enough satellite density that each satellite can see a neighbor.