>>49294691You can skip Brawly, only need to beat him before Norman. Winona is also skippable but since she enables Fly you'll want to beat her sooner rather than later.
After Mt Pyre, there's some backtracking to progress the game: Team Magma hideout is back on the route leading from Mt Chimney to Lavaridge Town and Team Aqua are back at Slateport City. I don't remember if any of this is explicit in the game, it stumped me as a kid but I've played Emerald so much I don't think about it anymore.
New Mauville is unlocked after the 5th badge, kinda hard to miss since you have to pass Wattson to get it.
Feebas is a cunt to catch.
Shoal Cave has a tide mechanic that you'll need to consider if you want to fully explore it.
Dive isn't as important as it seems, you'll need it mostly for story purposes or for initiating the Regi quest, so you can probably drop it as soon as you can fly to Sootopolis City.
Trick Master refreshes every badge I believe, but you could also do it all in one go at the end of the game.
Battle Dome is the best facility.