Learn Farsi: ترسِ او بزرگ نیست.

Absolutely! tars-ash uses the attached pronoun (-ash) and means the exact same thing as tars-e u. Using the independent pronoun او (u) linked with the ezafe just gives slightly more emphasis to "his" or "her" than the enclitic does.

In English we usually say a "great fear" or "intense fear". Is bozorg (big) natural here?

Yes, it is very natural. Farsi commonly uses بزرگ (bozorg) to describe the intensity or scale of abstract concepts like fear, joy, or problems, much like how we say "a big problem" in English.

I don't see any letters connecting the word for fear to the word for him. How do they link?

They are connected by the ezafe, which is a short "e" sound added to the end of tars, making it tars-e u. The ezafe acts like the English word "of" (the fear of him) but is almost never written in the Farsi alphabet unless the first word ends in a vowel.

Why is "is not" translated as a single word (nist) instead of using a negative prefix?

The verb "to be" is an exception to the normal rule for making verbs negative. Instead of adding the negative na- prefix to ast (is), Farsi uses the dedicated word نیست (nist) to mean "is not".