Don't know since I went in early fall. Sorry, but does it even matter if you get to skate?

Yes. There are several stops to People Mover, a few of them are relatively close to Campus Martius.

Lockers are available to rent (the posting I saw said they were free, first come first serve).

Yes. It’ll be open until March 3rd, 2019 and then reopen in November.

There is a variety of paid parking, including on the street, surface lots and parking structures. Depending on how long you plan to stay, the street parking would be your cheapest alternative. It might be fun to check out detroit's newest hotel, the Shinola on Woodward. There's also a Shinola store. If you're into street art, The nearby Z-Lot and Belt Alley might be of interest. There's murals on each level of the parking structure. If you like architecture, you must check out the Guardian Building, an Art Deco jewel. Hart Plaza near the riverfront has an interesting fountain and some sculptures. Well, there a few suggestions.

Everything, except food and possibly skating, is free in Campus Martius Park. If the "beach" is there, please know that it's not an actual beach. More like a lot of sand, with volleyball nets and such. No water anywhere. Still a fun time.

The park is free to enter. The beach is artificial, and not adjacent to water. Still a fun time.

Yes

I would park in the Z Parking Garage. It's a few blocks away in another cool part of town. Next to The Belt (alley). Depending what time it is stop at the Skip in the ally for a frozen cocktail. The garage is an experience in of itself with all of its painted murals.

There are no carriage rides in Campus Martius Park. During the week there are multiple food trucks and often have live music during the lunchtime hours. The Q-line now runs past the park as well.