coolant is full, that's a good news.
Fan working with A/C on, good.
No engine heat light showing, good.
without A/C fan might take time to start, because engine does not require much load in that case especially in the winters, don't worry.
so overall your car is behaving perfectly fine, nothing to worry about.
however, most important thing is to get engine oil, oil filter, air filter and gear oil changed (even if the previous owner has changed it recently, you should get them changed yourself so you can keep a record in your own maintenance book).
and rest of the things you can get them changed as problems show up no big issue.
i don't own a Civic, so i cannot recommend which engine oil is best for it, but i think 5W/30 or genuine Honda engine oil and gear oil would be good.