Thank you for making your first post here! Welcome to reef2reef
indeed, rinsing out a reef tanks sandbed with tap water isn’t usual

but it gives the consistency we get here for these years.
heres my answers:
1. before you do the big move/upgrade job take out a test rock with attachments on it you don’t want, and sit it on the counter
take a knife, not any other tool but a knife, and use the tip to scrape away algae and be exacting, work around corals etc. debride and rasp off all the algae, rinse it away with saltwater.
then when the area is made clean by scraping in detail, rinse off that cleaned section with peroxide and let it sit a couple minutes. This isn’t a dip, we never dip anything here, this is spot application of peroxide on areas that formerly had targets but you cleaned them off with a knife and saltwater rinsing first. No peroxide goes on algae, it goes on cleaned areas you detailed that used to have algae
algae is handled this way, vermitids will just grow back. You can search the forum for vermitid tricks, they’re hard to beat. I can’t beat them in my system.
2. rinsed sand made safe isn’t any type of seed. It’s just plainly rinsed 100% cloudless so that it’s neutral and can’t cause any cycling issues by clouding. Any dry rock you want to add just goes into the new tank, alongside the old rocks you cleaned and moved. the new rocks uptake bacteria by being in the tank alongside the other rocks, no seeding is needed. Your old rocks carry all the bacteria you’ll need anyway.
3. if you aren’t using any old rocks at all, then you should cycle the rocks well before the move job in a brute trash can and verify they are ready before being made the sole rocks in the new tank. You should not toss the old rocks. Clean them, move them all over - new rock will give you uglies that lasts a long time and old rocks cleaned off are what comprises this whole thread, no cycling happened. If you must use all new rocks and no old ones then simply have all the new rocks ready ahead of time.