1- " Wanted" is "to want" in the past, so I want to buy a ticket means "I want to buy a ticket now", while I wanted to bu y a ticket means "I want to buy a ticket", but it is a past action.
2- I think you are referring to the verb. In this case: I thought the doctor took you home
3- I have had a long day -> to have in the past
4- Look at this: I like football (football is one of my favourite sports)
I like to travel -> like + infinitive -> travelling is one of my favourite hobbies
I think you should revise the Simple past, so everything will be clear