Hi Kevin! I have crossed out or highlighted any pure grammatical errors. The numbers in parentheses indicate phrases that are not grammatically incorrect, but have multiple variations, which I have listed at the bottom:

Simple Present/ Present Progressive/ Simple Past

I have to use the Simple Present if I like to write something which is repetitive, if something happen in the present or in a general statement.
signal words are: every day, sometimes, always, often, usually, seldom, never, (3)first... then

Present Progressive: He's now learning English. (4)He's not learning English at the moment. Is he learning English?

I have to use Present Progressive if the action is at the moment I'm speaking or writing.
signal words are: now, at the moment, Look!, Listen!

Simple Past: Yesterday I saw a great film. (5)In 1996, I was borned ( I think "born" is more correct.) in Fulda.
Did I wrote the last sentence right?

I have to use the Simple Past if an action started in the past and is ended.
signal words: last..., ... ago, ..., in 1990, yesterday

(1) It sounds more natural to say: He doesn't always learn English.

(2) You can also use: "Does he often learn English?" However, both variations sound natural. 

(3) the "first...then" construction in English does not indicate repetition. It indicates causality. "If I first do something....then that will cause me to do something else."

(4)If you really want to stress that he is not learning English, you can use: "At this moment he is not learning English." However, they both sound natural in English.

(5)Unlike in German, it sounds very unnatural to mention the year at the beginning of the sentence when stating when you were born. Such sentences almost always begin with: "I was born..." the rest of the sentence can either be the year or the pace you were born in. If you want to mention both, it sounds more natural to say "I was born in (year) in (place)." For Example, I would say: "I was born in 1981 in Eugene, Oregon." However, I think there will be different opinions on this between native English speakers based on their nationality and region.

Simple Present/ Present Progressive/ Simple Past