Update: SpaceX has apparently decided to skip production of SN17 - SN19, and go straight to the build of the designated first orbital Starship (SN20). At present SN16 is sitting, mostly completed, in the High bay building at Boca Chica, ready for pressure testing. SN16 is scheduled for a 20km high flight.
SN15 is still on the pad under going refurbishment since its successful flight, at least one engine has been removed for examination or replacement.
On the Integration Tower build, SpaceX has been pre-fabricating complete sections of the tower and overnight rolled out the second tower section to the orbital launch area. It will be lifted into place by the newly assembled mobile mega-crane. There are three more tower sections nearly completed at the build site. That means five of the Tower's rumoured seven sections, are pretty much ready for stacking.
For those interested, there are several new videos up on Utube of build progress, one of which includes vision of the Booster methane distribution manifold, which is a real work of art in stainless steel. This manifold, at the bottom of the methane tank, carries fuel to each of the boosters Raptor engines. See NASA Spaceflight Utube channel for details.
Link here:
https://youtu.be/KWaSBJnSYGE