Canada – concurrent Chinese visas

I already have a valid Chinese 10-year L-type visa obtained in 2018 when I traveled to China last year. Now I am planning a sightseeing trip for 2 weeks, followed by a stay at a university where I would teach for UNPAID for 3 weeks (a total of 38 hours).
The main objective of the trip is tourism but, from my reading, I think I need an F type visa for those 3 weeks.
Question 1: Can the Chinese visa office issue two visas that are valid at the same time? (A new type F and my current type L)
Question 2: Could my L-type visa be suspended and then reinstated?
Question 3: If I have to give up my type L visa, can I travel for 3 weeks with type F?