How to unlock the following characters

I did this just tonight (Xbox 360 version, for what that's worth).

Maria does get a super speed boost at the beginning of the race, but if you floor it and manage to keep from hitting the sides of the track, you will eventually catch up with her. I don't know if she corners poorly or if her top speed is less than yours, but she doesn't maintain her early lead throughout.

The steering and the camera are the major problems here. You will generally want to make frequent/rapid small adjustments rather than really throwing the stick to one side or the other. If you do that, you'll tend to make an overly tight turn suddenly and hit the side of the track. It takes a few practice runs to get the hang of the curves - the camera tends to fail to keep up with these, so you won't have a clear idea as to where you're going until a few seconds after you turn.

If you can stay on track, you can catch up - I tended to pass her or bump into her between the last checkpoint and the finish line, generally speaking.

An Alternate (Cheesy) Method

I discovered after some races with Ghost Rider that sometimes he got off-track and took forever to finish the race. Some further investigation shows that the AI actually drives the course "legally" - their time changes depending on what kind of traffic and so forth they encounter.

So, what good is this information? Just park something in front of NPCs you intend to race. They can't quite figure out how to get around it, and will give you a commanding lead while they work it out.

In this specific instance, Maria Hill is on an elevated track. If you jump down to the vehicle call-in point and summon a helicopter, you can land it on the track in front of her with a bit of effort. As much as possible, try to keep your side of the track clear. Then, when you start the race, she'll run into it and give you an advantage.

This is obviously much, much easier on the ground, but it is doable on her track. I used this trick on the second race with her to great effect.

I'm out of these races now, but I do wonder what would happen if you parked a big character (ie, the Hulk) as your co-op partner in front of her....

These boxes typically have some device nearby which you can activate to open them. Some actually have multiple activation triggers. One in particular on one of the skyscrapers has three different "puzzles" you have to solve in order to open it.

I find there are little red lights nearby which turn green when you've solved some part of the opening sequence.

Usually you'll need at least one character's skills, but frequently you'll need multiple. Generally speaking, these are going to be tricky or impossible to open until you've unlocked free play for Manhattan by clearing all of the story levels.

At that point, you can switch characters at any time by holding down the "change characters" button (ie, Y or Triangle on Xbox 360/PS3).

Prior to that point, you can switch characters at vehicle call-in points, but the number of characters you're going to need for some of these makes the extra effort not worth it.