Correct. When you have heavily armed troops (it doesn't matter if they are Regular Army or LAPD; if they are carrying M-4's or heavier, they are troops, not police any more) tossing aside the civilian-law requirements of warrants and probable-cause, ordering citizens to obey at gunpoint, then it's martial law regardless of how it's called.
Nope. Martial law has nothing to do with actions of cops or military.
It is a suspension of normal law, habeas corpus, etc. that makes the actions of the cops and military that you describe legal.
If martial law is not in place, the cops and military can still do such things, but their actions aren’t legal.
IOW, martial law nothing to do with what is done, only with its legal status. The courts are typically closed, and offenders can be tried by military tribunals, not civilian courts.