At the stage your at and trying to figure things out you should look for the out of print but floating out there on the internet a magazine called Home Power.
Go back to when they started to publish in the late 80's there all on PDF's and you can see the pit falls and the how to stuff and come away with a great understanding and how to or not to make things work.
The earlier first few years of the magazine were the magic of making it work hands on vs later years more commercial focused.
Oh also if you do look and find the earlier copies on PDF's buckle up as your going to say they look like some dude printed them up off a home computer and well he did hence the title of the magazine.
The information in those old first few years is where the real value is.
Yes there are some completely out dated ways of doing stuff there as well but what your looking for is still relevant.
https://www.homepower.com/archive-browse
First and foremost please be safe.
Don't mix batteries of different amp hours and or types.
Have a fuse that cuts off batteries to inverter for safety.
On a 12 volt system lower gage wire is not only for safety but needed to move those amps to work load as in the inverter.
But again you need a more robust sinewave inverter.