I just started and my house is a mess, anyway to storage? Or isn't that in this game?
You eventually unlock a huge storage locker that you can access from within your house. I think you unlock it when you pay off the upstairs floor - it's one of the new things introduced in the Welcome Amiibo version. (You also gain the ability to move items around using the touch screen.)
You can also store items in the exhibit rooms of the museum (after you gain access to them), or in the post office by mailing items to yourself. Or you can just add an extra player-controlled villager and store things there.
I'm not able to put furniture on the ground outside like in NH.
Sure you can - it just doesn't look like anything, and Isabelle will tell you that the town is a mess.
Probably need to upgrade Nook for the wetsuit, at least if it's the same as in NH.
You can occasionally get the wetsuit from Tortimer Island, but you have to play the minigames many times before you'll be able to afford it.
Or you can just go online and see if someone will trade you one. I might suggest the ACtrade reddit, but I'm not sure if everyone there has moved on to ACNH already. Also the mods are vicious and you can probably expect to be banned if you stick around for long enough. (ETA: Apparently r/AnimalCrossingTrading is where it's at now?)
ETA: Or you can just edit your save file and give yourself one if you don't want to bother going about things the hard way. :-P It's not really in the spirit of things, but reading what people have posted about ACtrade around the Internet, I'd probably prefer to do it that way. Running JKSM through Browserhax is quick and easy; you don't need to do a full CFW install.
I found am emerald, so you can craft here aswell? If so, cool.
Not really. You can use minerals to change the color of a small range of items, and you can use gold nuggets to get random pieces of gold furniture. And you can get models of fossils, but you'll probably want to finish the museum first.
Now I'm thinking about picking up the 3DS version to play in bed before I go to sleep.
Have you considered Pocket Camp for Android? There's not much to it - meaning you might actually get some sleep.