Why not?
If it's on my PC, the PC could die and I'll loose access. If it's on mobile, it could be stolen even.
Another question, does mycelium and LocalBitcoin allow to sell bitcoins and have the $ in my bank account?
Because if you don't have control over your wallet's private key or backup phrases, you technically don't own the bitcoins; which is the case with most if not all web wallets. and yes, if you lose access to your PC or your mobile device, you lose the bitcoins; unless you back up your wallets, which is something a bitcoin owner should do.
Mycelium is a wallet.
You can sell and buy bitcoins on Localbitcoins.com with your bank funds.
So out of all the wallets out there, which would you say are the top two?
I have installed MultiBit HD on my PC, but it doesn't have mobile version.
I have installed Copay as Chrome plugin, desktop app and mobile app. They all sync up.
I have installed Mycelium on my mobile. I did the back up but it's not clear when the app says to store the master seed off the phone... so I don't know how to proceed.
I know that mycelium offers local traders. Is this a good option?
There are actually no "top" wallets, it's just mostly comes down to personal preference. But I think on PC, the most used one is Electrum; whereas on android I think its mycelium and copay (not sure).
Havent actually heard of MultiBit HD, so I can't comment on it if its good or not.
I downloaded mycelium too check. click on the ellipsis(vertical triple dots)

on the top right of the screen; then click on backup.
I honestly havent used mycelium for trading, but mycelium has quite high reputation on the bitcoin world, so it would probably work well. no promises, though. as I personally use localbitcoins when trading low amounts.