A few comments about the plot holes you mentioned.
"Chasing" someone through a Turnstile doesn't make any sense. When Sator Inverts to escape Ives' guys, let's say he does this at precisely 12:00, then 5 minutes pass and Ives and crew go through to invert and "chase" him, it is now 12:05. So if they know how inversion works which we know they do, why do they not just wait outside the turnstile after inverting until 12:00 when Sator would could out of the Turnstile and get him?
As others have mentioned this is not time travel. Sator walks in at 12:05 and as soon as Sator is on the other said he becomes inverted. As one minute passes for Sator, it becomes 11:59AM. If I enter this at 12:05PM chasing him an wait a minute, it is now 12:04. However, Sator somewhere doing something at 11:56AM. If I wait another few minute in front of the turnstile it it is me existing in the turnstile at 12:00PM, but Sator is off in the world inverted too. He is doing something else and it is now technically 11:52AM for Sator. If Sator waited at the turnstile and I saw him on the other side I could have grabbed him, but he did not wait. We know he had turnstiles in other locations and as P was told before he entered one for the first time - NEVER enter one if you do not see yourself entering on the other side at the same time.
This is even more glaringly weird in the scene in Oslo where TP goes into the Freeport first to "clear" it. He fights himself and goes into the Turnstile first say at 12:00, and then he hijacks the Ambulance and waits for Neil to arrive, say at 12:05. But Neil "waiting" for TP to clear the Freeport while inverted means that his inverting "after" TP in backwards time would mean he would be coming out BEFORE TP in normal time. If Neil enters the turnstile at 11:55 then that means he would have beaten TP to the Ambulance, or TP would have had at least had to pass him.
I think what I said above applies to this too. The time differential is not 1:1. It is not time travel, it is someone being inverted in normal time. The world remains normal, you are inverted.