Hi @mzoli, and welcome!
You don’t have to worry about the GPME errors. You can ignore them. However, if you want more information, look here:
Regarding
It looks like your database is out of date. You can use pacman-mirrors to update it when necessary:
pacman-mirrors --fasttrack 5
This will select the 5 fastest mirrors for you.
Then you need to update, either with pacman or I recommend using pamac:
pamac upgrade --enable-downgrade --aur --devel
I recommend pamac instead of pacman because it’s developed by Manjaro (devs) for Manjaro and just takes care of more things for you. For more information, see the man page:
man pamac