BIGGG mistake

Only joined games to trade before today. Joined first lobby game to play and second and ... wow, I was not ready for the speed.

Was killed in about game #12 by another player. Some not nice but earned text was sent my way. At that moment, I instantly understood. I never accepted the in-game invite to ally. I was trying to keep up with the pack and wasn't reading. I had wondered why the movement Pattern made little sense. They had been running and leaving the game. I was simply crushed with the reality. Going back over the log made everything clear. Some players died by cows and were weakened or stunned by me.
How to apologies, make it right?

After some time, I joined another game and asked how to ally.

If you were in one of those games, I sincerely apologize.

I wouldn’t sweat it

I don't think you can

Stun or

Weaken other players in the cow level. It might be something else that may or may not be related to you.

It isn't going to be possible or realistic to apologize. Take it as a learning experience for the next time. Just remember to always hit 'P' in a group game to bring up the party list and make sure everyone's showing green. You can also find tutorials on YouTube about etiquette of group play, especially for pick-up groups (PUG). gl and don't feel too bad. In the end, it's just a game.

As noted above, you can open your party screen to join the party.

Alternatively, you could go to your game settings and enable auto-party. That way, whenever you join a game, it takes care of that for you and you'll simply end up in the party by default (most of the time anyways..occasionally it bugs out).

You yourself could not have stunned or weakened any players unless you actively hostiled them first (which I doubt as that's the same screen as partying them) or they hostiled you (at which point that's their own fault). The worst thing you could have done is to make some mobs move in a direction they didn't want them to (which may kill the naked unprepared leecher) or steal the occasional kill (which costs them the xp for it).
Both obviously aren't ideal but also nothing to feel so bad about after the fact if it was a genuine mistake..things happen. Just turn it into a learning experience (as you are here) and make sure to party up next time.

As for movement patterns not making sense, that's normal. They actually typically do, it merely doesn't always look like that when following along. Experienced players/chain runners will pick their patterns based on what they deem to be the ideal route to clear as many mobs as possible/champ packs primarily as fast as possible which is rarely a straight line and will typically result in skipping some mobs/smaller packs.
Add in the fact that in pug games, you reliably end up with a few people who don't care about the party and go their own way, branching off that same path and going somewhere else entirely and it looks beyond confusing all in all. Even more so because those people WANT to be on their own so if you try to follow them, they'll typically go nuts and

Teleport all over the place in a confused effort to try and lose you.

If it's split farm, ask people what's already taken and ignore these locations. Don't farm in trade games, it's considered bad manners and host may try to kill you. You also may use option "automatically join group" in settings, or press "P" to open group screen and join others.