I could use some help with these sentences:)

I am writing a letter of motivation for university, and I would love to get some help with the following sentences. First of all, is 'to' correct in the first part (before 'tell you why I would love to study at..')? Or should I delete that, or replace it with something else?

Second of all, I am not sure if I should use 'a way of learning' or 'to learn' in the second sentence. Which one would sound better/more natural?
And last of all, is 'that' correct after 'people'? Or should I write 'who'? If they're both correct, which one sounds more natural?

Thanks a lot for your help in advance, I really appreciate it.

Kind regards,
Leila

Here are the sentences:

My name is .... and I am ... years old. I would like to use this letter as a way of introducing myself and to tell you why I would love to study at .....

Ever since I could, I have always loved to read. Reading is for me not only a way to escape from reality, but also a way of learning about the world and about all the different people that live in it.