It appears you are using a piggyback "fuse tap", I can see one in a photo you posted earlier.
As long as the circuit you tap off is rated reasonable high, that should be fine.
Only fit the upper fuse first (your 5A one) and make sure your new device works - if it does not, the tap is the wrong way around. Then fit the original fuse in the lower position.
For grounds, try to fit them on a metal bolt that is directly in to metal parts, so you get a good connection to the chassis.
Clean off any paint immediately next to the bolt hole so there is bare metal, eg. for an area like a washer.
I usually fit a crimp eyelet terminal the appropriate size for the bolt or screw, plus adding shakeproof washers ("Star washers") both above and below the terminal eyelet.
The sharp edges on those cut in to the metal and help ensure a good connection. Put vaseline over the metal to prevent rust.