Couple of task strategy questions

Couple Qs for the tasky community:

The other night I was playing online against a guy with a team of Task and Akuma. The guy would get in for free with charging star + tatsu assist and then pressure with spidey swing > air spidey swing into air normals, which point he’d land and be just about ready to start the charging star + tatsu shenanigans again. How do I punish this? I tried to mash back+H on the ground to grab him out of it but the frame data was not in my favor. Should I / when should I pushblock? Should I be chicken blocking and OS throwing?

Also, what’s the best way to use cold star for combo extensions? I thought I saw someone on a stream OTGing with down arrows in the corner and then doing the first part of the unblockable, then connecting with QCF+S. It seems as though cold star lifts them too high for QCF+S to connect under normal circumstances. EDIT: watched this again - what they actually did was hard knockdown into down arrows OTG with coldstar, then the first portion of unblockable linked into charging star cancelled into QCF+S.