I am going to guess you have a tendency to take things very personally.
From your point of view, your parents offered to pay for everyone’s take away, except yours. But from their point of view, there was 3 places to visit. It was easier for your mum to pay at the places she went and you pay for the place you went. Only you wanted something from where you went. Your mum thought she was doing a favour and saving you money. Doesn’t sound like her intention was to say ‘we will pay for everyone else’s but not yours’. She obviously rethought that and felt it was only fair she paid for yours too.
However, in this situation, I think you were wrong. You offered to pay for a takeaway so they didn’t have to cook. It ended up costing them money and you are still annoyed. When your mum said you could just pay for your own, you should have insisted you would give her the money. I pay for loads for my adult daughter. But if she offered to pay for a takeaway so I didn’t need to cook, then it turned into me having to go out and collect most of the food and pay I would be thinking ‘what was the point in this?’. But I would also point it out to her. In a lighthearted way.
When it comes to the movie, again, you weren’t in the shower. Because you could clearly hear what they were saying. People had been doing their own thing. You went off to get a shower, we’re out of the shower but still faffing around when you knew people were sat waiting to start a movie.
I would guess your family, often feel you are easily offended or they have to tip toe around you. If I were at my parents I would have shouted up to my brother ‘hurry up, we are starting the movie you will miss the beginning’ and put it on. I wouldn’t have sat round waiting when we had no clue how long he would be. or if I was in the shower and I could hear them in the living room, I would have shouted down I was going to be 5 mins.
But the conversation they had either was a joke, or a group of people that don’t feel they can be direct with a person so coming up with ways the head off their reaction but fed up of waiting.