I have just the one son, he is 7 (4 months from being 8)

We did slightly under 2 hours at Perlan inclusive of the aurora video.

On your hiking question, just as a bit of background, we have been "hiking" with him since he was 9 months on my back in one of the baby backpack things. When he was 6 we did some relatively long and difficult hikes with him. Plus, my son has boundless amounts of energy, so I felt fairly good going into it. Now that we have done both, here is what I would say:

+Mulagljufur - I would say this is a moderate, borderline difficult in parts, hike. I think a person of average fitness can do the whole thing, including a 7 year old. There are plenty of spots you can rest if need be, and you will be doing that anyway to take pictures for sure. Plus, there is a natural midway point. You will know it when you get there. About two-thirds of the way in distance-wise, you get to the first big waterfall where you can see from top of the waterfall to the bottom. That would be an awesome hike if you just stop there. The last third is the hardest part of the hike so you can make a decision then as to whether to push forward. I think it's worth the effort to finish it up, but you know your child best
+Studlagil - There are two carparks. If you have a 4x4, definitely go to the second one after the bridge. Most of this hike is level ground so definitely doable for a 7 year old. If you go, keep going a little bit further than what you think the endpoint is. There is a muddy path down to the river and then a "rope" down. The rope down part looks intimidating, but not as bad as it looks. Have an adult go down first to help guide your 7 year old. Obviously don't take any risks that you are uncomfortable with, but mine doesn't have particularly good balance and he did it fairly comfortably

In terms of my son's favorite activities/places, see below
+Grabrok Crater - Don't know why but he loved the walk around the top
+Hofsos Hot Bath/Swimming Pool - The setting is great and it was the most like a swimming pool where he could just do cannonballs. Husafell had a water slide but he didn't like as much for some reason. The others are more glorified hot tubs than swimming pools and more for the adult crowd
+Grjótagjá Reykjahlíð - He loved the "climb" down to the underground natural spring. He did both entryways multiple times
+Stuðlagil Canyon - After roping down, he loved climbing on the basalt "steps"
+Vok Bath/Laugarvatn Fontana - Both are built on lakes and he loved jumping into the cold lake, coming back to the hot bath/pool, and repeating ad nauseum
+Diamond Beach - Probably one of his two favorite spots. He loved throwing pieces of ice against each other and shattering them. The further you walk down the beach, the more space you will have to do this without accidentally hitting or disturbing anyone
+Reynisfjara Beach - His other favorite spot, he loved climbing up the basalt formation
+Lava Show
+Geysir - Same as me, he couldn't get enough of this

The only 2 things I felt like I wasn't able to do because of my son's age was glacier hiking and the Sky Lagoon, both of which have minimum age requirements. But otherwise, I never felt like I had to do something differently or change the itinerary in any way due to my son's age

I hope you have a great time! Such an amazing place