“A bug on a log is less.” So her dad by a bug.
Simple past tense! Also, add a comma behind {so}.
“A bug on a log is less.” So, her dad bought a bug.

Nell have a pet bug.
Still the tense problem. If you are telling a story, use simple past tense please.
Distinguish {it’s} and {its}.
Use the plural form of {thing} because the good things are more than one.
Every pet had its good things.