Can you rent bikes there?

I don't believe so. You can rent bikes at Buffalo Bayou Park on the Sabine street bridge if you are looking for something close by.

Spotts Park off of Heights rents bikes, as well.

Did not see any rent.

Yes, there are a couple of bike stations around memorial. Check their website for an accurate spot.

Yes. A BCycle station map indicates two rental stations within Memorial Park, https://houston.bcycle.com/station-map. A station location app is available, too. Consider checking the Memorial Park website to assist in planning your visit.

Nope. But search near by.