Are there in public showers around Memorial Park?

I've used the showers at the pool ($0.82) and at the running center ($0.75).

There are in the tennis building on the three mile jogging loop. There are also paid showers in the all trails building by the train tracks.

Yes, in the tennis center, 50 cents/shower.

Yes

there is a public one on the 3 mile loop near picnic lane light. though it's not covered so maybe swim trunks??

Yes. They have a charge for towels or locker rentals (tennis center). Not necessarily for the shower use themselves. The golf center also has showers, but I am not aware of a charge there.

Yes. There are several at the tennis center and two at the swimming pool.

No