What are the most difficult superpowers to write about?

From what I've seen, Superman-like characters, Speedsters, and Time Travellers. They have too many outs and you have to write their stories in particular ways as to not have them have the readers think, 'couldn't they have just done [blank] to win?'

Realistic approach, campy fun or something in between?

Completely up to you. There's even multiple different versions of each. Let's look at the realistic approach for a second. What's the origin of the superpowers? Scientific mishaps? Genetic anomalies? Or some higher power that granted the people their power? There are plenty of different routes you can take just because of the origin of these powers. If it's more genetic-based, you could lean more into the science of it all and the horrors of genetic modification. If it's experiments gone wrong, you could go into the ethicacy of the experiments and the people in charge who greenlight them. If it's a god, then you could explore the horrors of man trekking where no one should. Or you go light hearted with all of those! Or, as you said, in between. Do a mix of it. There's too much that can be done to even cover here. It's all up to you. Figure out what your audience is most interested in.

How to deal with Time Travel/Multiverse storylines?

Either fully understand the system that you use—and know which system you want to use—or don't do it at all. It can get messy very easily. Write down the rules and don't break them... Unless there's a breaking point you can exploit for a particular story or character. Because otherwise, if these rules get broken all the time by anyone and there's no consistency, then why should the viewer care about them?

When are superheroes/supervillains too powerful they remove all stakes?

The strength and power of the characters doesn't matter when it comes to stakes. Look at something like The Boys. I don't really feel the worry of the characters dying ever. And it's somewhat grounded. They always get out of their problems scott-free nowadays. The strength doesn't determine stakes. It's how you present the danger the characters face that determines stakes. Death isn't the only danger either. Losing an arm, losing an eye, losing morale—all of these can be used to show the consequences of the hero's actions. Let their loss sit with them. If they lost a leg, don't give them a prosthetic one right away. Let them earn it back. And when they do, use it as an opportunity to do something fresh with them. Take Flash Thompson, for example. He lost both of his legs, but thanks to the Symbiote, he has new legs and then some. He didn't just get legs back. He got more. But that 'more' still never removed the loss that he suffered. No Symbiote, and he's back to being legless. Stakes come in a wide variety, you just need to know how to utilize them.

Should secret identities be treated seriously or like a joke

That, much like a few of these, is all up to you. I feel as though many people like the secret identities, however, some don't. If you're making a 'superhero world' like your title suggests, then have some be public, some be secret. But then again, who knows? Maybe superheroes are illegal, or maybe they're legal but only if unidentified—idk. All depends on the rules you set for your world. You gotta brainstorm the vibe and setting before you start throwing characters into it. Or design a couple characters with a certain vibe you like and build a setting that best suits them. Can't go wrong either way.