Are these translation right?
 

"I don't want to read"= "私は読みたくない"
"I wanted to read! " = "私はよみたかった"
"I didn't wanted to read" = "私は読みたくなかった"
"I didn't read" = "私は読まなかった"

Correct, well mostly.
The part you got wrong was actually in your English.

"I didn't wanted to read" should be "I didn't want to read"

In your Japanese you could probably omit the 私は part, but i guess that depends on context.
But it's good to try to use pronouns as little as possible anyway.

Eheh yes.. Thank you! I'm studying english too as well as japanese, and I really appreciate when someone corrects my english besides my japanese :D

is this correct?

だから、私は日本人の友達欲しいです。= so, i want to have japanese friends.

だから、私は日本人の友達が欲しいです。

You should add が .
Its natural.