Does anyone have any advice on using umbrella rigs for striper/hybrids? What depths do you typically troll them at? What size jig heads are advised? Can you use them to locate fish and then try to go back and catch them?

I use 1/4 oz. up to 1 oz. jigheads. It depends on how deep I want to go. I also add from 1 oz. up to 6 oz. of clip on weights in front of it, to get it deep with a short amount of line out. Boat speed is from 1.5 mph to 3 mph. It is a trial thing. Find an area on a lake that doesn't have a lot of trees, stumps, or rocks and start trolling at different depths. When you see your rodtip jump a little, you know it is probably bouncing on the bottom. That will tell you how deep you are. I typically troll between 14 to 35 ft. deep. depending on the lake and how deep I mark the fish. It is great for locating fish and then going back to slab or drop live bait down. Saves gas if you do that also.

It takes some R&D to know what you are doing depth-wise. Like said above, trial and error are the only way to truly learn. Having a line counter on the reel helps a lot in repeatability once you figure it all out.

Funny how these things are so widely accepted here now. I remember a fella who makes them came on this site a few years back and got trash talked by a lot of people claiming umbrella rigs were somehow unfair or cheating, enough that he left the site all-together. Seems now they are widely accepted. Funny how people evolve.

It just takes 1 or 2 people that are popular to the public, who are willing to try something new, to start a stampede over the edge of a precipice. lol

Ya, to me it would seem like a cheaper and more fun option for locating fish than investing in a really expensive sonar unit. Not saying it wouldn't hurt to own one, but right now, I just have an old fashioned set up.

Do the fish spook if you drive over them and then try go back and find them at 15+ feet? Also, do you typically find these fish suspended randomly or pretty tight on structure? I ask because I think it would affect how you might strategize posting up on them.

Another kind of random question, what colored lures do you use? Do they need to all be the same color or is variance good?

Stop on a point, hump, creek channel, etc and cast the rig and let it go to the bottom. Then just slowly reel it back into the boat. That method works for me. Trouble is that I rarely ever use it. Might try it again next time out.

There are different size umbrella rigs. I have some that are 6 inch ones, and different sizes up to 31 inch ones. The smaller versions are mainly designed for casting but can be trolled. The larger ones are very difficult to cast. I have some that are 31 inches across with 8 inch leaders on the perimeter and 16 inches long in the center leader. No way I would try casting that.
If you are not careful with the larger ones, it can get expensive in a hurry. That's what I like about my down image sonar. I can tell a tree from a bait ball before my big rigs get into it, and get hung up. DI is well worth the money to me.
I have noticed at times trolling say northern direction I get I bite, then turn around to troll same path but southern direction and no bites. Or east vs. west. Sometimes it doesn't matter, they hit it regardless. It is trial and error each day and hour. You have to experiment to see what colors, speed, depth, direction, and area works right then. No one can say do this, this, and this, and you will catch fish. You have the right idea, though.
Same lakes on different days will be different results. Different lakes on the same day will be different.
I use different colors on my rigs at the same time. Up to 4 different colors, to give the fish a choice, then switch all the baits to the one color they choose the most often.
Is this right? I don't know, seems logical to me. At the same time, some would say, if the baits are not the same, the fish would recognize the baits aren't similar and not be attracted or scared off.
At times the fish do scare off some, when you idle over them, but normally not. They are on that structure feeding and will chase the smaller fish who are scared by your boat. Boat has bigger profile than shad which are usually shallower than the bigger fish, so they scattered willy nilly which makes the predators attack.
Normally idling over them isn't as bad as half throttle or on plane.
I am not an expert, others have other ideas that work for them. My

Which reels and rods do you use to troll with them or cast them?

My dedicated rod/reel is a 7'6" x-heavy swim bait rod with an Abu Garcia Revo Beast. 60lb braid