great question! the reason you need to use "the" in those sentences is because it is inferred that there is more than one person. She swims the fastest means that there is more than one person, infact it means that there are atleast three swimmers. If it was just her alone we would say "she swims fast" and if it was only her and another swimmer we would say "she swims faster" but since it is said "she swims THE FASTEST" we know it is more than 2 people. I know this can be confusing, hope I am not confusing you more! hahah As for the last part, I personally think that the correct one is "the things I like the most" if you are talking about more than two things, or for only two things (chocolate or vanilla) it would be "the thing I like better".

I swim the fastest

@Dark Panther it should be "I swim fast/faster" or you can write it like this " I am the fastest swimmer " is that correct Mr. Adam81 ?

Pronoun + verb + THE best/fastest/most awesomely... I like it the most. But I do feel like sometimes when people speak fast, they'll leave out the "the".