Rabbi Frand recently gave a shiur on Tefilla Bitzibur (it refers to shmone esrei) and what is considered Tefilla Bitzibur (it was one of the parshiyos in the latter half of sefer bereishis, you might find these shiurim online somewhere). He brought down shittos that run the gamut from, one must start shmone esrei with the tzibbur for it to count as tefilla bitzibut to the other end of the spectrum, as long as someone from the tzibur is still davening shmone esrei you can start and it is considered that you davened bitzibur and shittos in between.
I’ll leave the other questions for others.