Is this worth fixing?

I have a iPad Air (A1475) it has the cellular option.

My unit has 3 problems, my home button appears to work yet seems sunken in, the screen has one spot not cracked but there is a bit of a dark discoloration under it about the size of a pencil eraser, and lastly my battery is completely wonky, I plug it in let it charge to 100% it drops within 20 mins use to almost zero, I replug it in at say 15% and it jumps to 70% type thing.

https://ibb.co/dgjzYv is a pic of the spot on my screen if it helps.

I considered coming here buying the new home button, battery and I don't know if I need a digitizer screen or a new lcd screen?

Is it worth fixing? Even though I do have some experience taking stuff apart replaced a few iPhone batteries, fixed ps3/wii, wire up guitar electronics, so in general I am not afraid to do the work the thing is wonky anyway's, just trying to decide if it's worth fixing and based on my screen and that one spot is it most likely the digitizer or will I need a new LCD?