Welcome!! I do hope you enjoy the movies and fandom!! Your timeline seems to be missing Thor 2, and the chronological watching order should be:
- Thor 1
- Avengers 1
- Thor: The Dark World
- Thor: Ragnarok
- Infinity War
That Loki is/was tortured around/during Avengers 1 is canon! And so is the fact that the scepter he was using through the movie was also influencing him! Both of these are made pretty explicit and shown on-screen, though it’s never talked about or referred to again outside of the film, so many people watching casually are likely to miss or dismiss it due to his role as the main antagonist in the film.
At the end of Thor 1 Loki fell into a wormhole, then in that same movie we are shown in the credit scene after the film that he survived, but he isn’t exactly looking too good:
This follows into Avengers 1 and it’s typically accepted that it takes place around a year or so after Thor 1.
In Avengers 1 Loki is implied to have spent his time in space with ‘allies’ (later revealed to fall under the Ultimate Big Bad who is Thanos, someone who can and has used torture on-screen on numerous occasions to get what he wants). The film opens with it being revealed that Loki will be allowed rule of Earth in exchange for the Tesseract (which he has the unique ability to obtain), and is able to use the army his 'allies’ provide to complete both sides of the bargain.
Upon his arrival at Earth he looks and acts disoriented and crazed, attacking agents and using the sceptre he was given by his allies to mind control a few people. He stumbles and can be seen sweating profusely during these scenes as well as contradicts his position through the previous movie that he didn’t want to rule. He also uses an oxymoron about freedom and proceeds to leave hints at his plan through the film, but that leads into the theory that he wasn’t trying to win with his invasion and is open to interpretation.
Despite coming from 'allies’ he essentially looks in worse condition at the beginning of the film than the end when the heroes have defeated him, including chill non-hostile behaviour immediately after losing.
Loki is only shown conversing with his 'allies’ once, and we are shown he is doing the invasion under duress (threats, physical harm, heavily implied psychological harm) which is why his forced cooperation by them is explicit.
Deleted Avengers 1 footage tells us that the 'allies’ had a telepathic link which caused pain and had him being monitored through the course of the invasion too but those scenes aren’t canon canon.
Here are a few other posts about this with gifs detailing symptoms and going into theorizing into what torture was involved because while we know Loki was tortured we’re not given many details, and a lot of people deny it. (x) (x) (x) (x).
It’s worth noting that this never being addressed in-canon again has basically resulted in the MCU retconing it years later and deciding Loki was motivated completely on his own with the invasion and was using Thanos to achieve the goal of gaining power because he’s powerhungry and has control issues since he was a baby apparently (they also got rid of a few other backstory things of his), but that’s kinda not what the narrative Thor 1 and Avengers 1 tells us on-screen, so it’s open to however you wish to interpret it.
