For talking while doing something, you could do:

So in so fumbled with his fingers, then said,”Well, it’s hard question, and I don’t know what to say.”

You could do something like that. 
Hope that’s helps!!!

Hey! I’m currently writing a story as well, and I have had a lot of dialogue practice from it, so…

For dialogue, what I like to do is to put movements in between, or use it instead of dialogue tags. For example, using my characters:

Kali fidgeted in her seat, nervous. “Are you sure that this will work?” she asked cautiously. (this is including a dialogue tag)

Delyra smiled. “Of course it will!” She gestured with her hand at the letter she was writing. (this is excluding/replacing a dialogue tag)

You can use movements to naturally break up long bits of dialogue, which can make it flow smoother.

As for action scenes, I’m not that experienced, but from what I’ve written of dramatic scenes, using short sentences can emphasize certain things, along with some long sentences. For example:

She parried the movement with her sword with ease, practiced from her many hours of training. This opponent would be no match for her, like always.

She was wrong. (short phrases like this as a separate line can emphasize realizations and make the pacing of a fight scene feel faster)

A flash of white blinded her for a moment, as the sword glinted in the sunlight. Her breath caught in her throat, having just managed to dodge it. (adding visuals and sensory details can add)

But not completely.

The sword had managed to graze her side, and she knew that if she received more injuries, she would be worn out quickly. She had to make a decision, to end the fight, fast. (intertwining thoughts with the movements)

She aimed at the opponent’s side, and they moved to intercept.

And at that perfect moment, she struck forward.

~

Anyways, I hope this helps! Your superhero au sounds really cool, and I’d love to read it if you want to share.

For action during dialogue, I would recommend shifting between different synonyms of “said” and then occasionally adding in a bit of description of what the charries are doing. For example:

“Splendid, except the map doesn’t make sense,” he said.

“It’s good enough,” she returned, twining and untwining her fingers, over and over again. [returned instead of said, to give it variety, and then a comma to introduce what she’s doing while she’s talking]

“But if we lose our way…”

“We know it anyway,” the innkeeper interposed, standing up.

“All right, we’ll try it,” Tyron agreed. [And then the next thing after this should probably be “said” again, to keep a fair level of consistency]

For action, I agree with Moon Wolf that short sentences are very effective; using short paragraphs can also build things up, though it’s better not to use too many or the writing starts getting disjointed and disruptively dramatic. Sometimes long paragraphs are actually better; you can build up a lot of tension and action within them too. Anyway, hope this helps – your universe sounds fun:)

Does anyone have any advice on “Show, don’t tell”? I know I should do it, but I have trouble executing it.

Is there anything specific about “show, don’t tell” that you don’t know? Because personally, I think it’s hard to find the balance between both, when to show and when to tell.
But anyways, if it’s about “show, don’t tell” in general, here’s an example:
I went outside for a walk. (this is tell)

My hand reached for the doorknob, and I felt its cold brass against my skin as I turned it, the door opening with a reluctant creak. The cold breeze of winter greeted me, and the pale blue sky dotted with clouds contrasted the gray cement of the city around me. (this is show. Of course, it doesn’t have to be as descriptive, or it can be more, as long as you lay out the details like the reader is living it with the character)

And if it’s a question about when to show and not to tell, it helps to pick out the dramatic or important moments in your story, especially within a long scene that’s not super important to the plot. For example:

(tell) I recounted the first time I had experienced winter in the city. I had just moved in a couple months prior, and was trying to get used to the loud and fast-paced bustle of the urban life that I was unused to. (show) The bitterly cold winds blew in, scattering the dead leaves that had gathered on the ground. The trees lined the road like lifeless skeletons, tall buildings passing by as my footsteps hit the pavement, my breaths coming out in white puffs as I headed down to the local bookstore, eagerly hoping to get my hands on the newest copy of my favorite series. (tell) I was used to the warmth of the sun, even in the midst of winter, the apricity that would never leave. So it was quite surprising when I experienced my first sight of snow. (show) Snowflakes had begun drifting down from the sky, intricate little white crystals that floated down gently, landing on me as I turned up my head in awe. A gentle flurry had begun, much like the magic one would experience within a snow globe. I couldn’t help but stare as the snowflakes drifted slowly past my vision, each one a work of art, even as people bustled around me, continuing their lives like usual as if not noticing the wonder occurring before my eyes.

In this example, the first instance of using show helped to set the scene. In order to give an explanation as to what was special about this scene, I used a tell before and after, to skip to the important part in the next show, the “dramatic moment” that might be important to the plot.

I’m not sure if I explained it well at all, so feel free to ask more questions if you want!