Front gears won't shift
The derailleur does look too high in your second picture. The bottom of the outer cage should be about 2-3mm above the tips of the teeth big ring when directly over it. The cable is probably too loose which is preventing the shifter from pulling the cage far enough outwards.

I'd run through a step-by-step adjustment process as front derailleur adjustment can be tricky to get right.

Start by disconnecting the cable from the shifter and making sure the derailleur can move through it's full range by pushing it by hand. The spring is quite stiff so there will be quite a lot of resistance.

Check that the shifter and cable runs freely. Pull on the end of the cable and  work the shifter. I'd also check the cable housing to make sure it's inserted into the shifter and frame stops properly. You may want to take the cable out and clean and lubricate it, or even replace it.

A complete description of the full derailleur adjustment process is more than can be provided easily in text here. There are numerous videos and articles on the web that show you how to do it, but the best by far I think is the one by Park Tool Company: https://www.parktool.com/blog/repair-help/front-derailleur-adjustment.

BTW, I think the tab under the cable shift bolt seen in your first picture should be rotated 90 degrees anti-clockwise, so the finger goes over the cable.