1.
Yep, looks like you have too many
Presets for your screen.

Which screen size / screen resolution / scale factor are you using? If you're using a high scale factor then you could temporarily use a smaller scale factor to allow for more things on screen at once.

Is it a screen size problem or is there plenty of space above the menu except it somehow isn't aware of the start menu bounds for some reason and is thus hidden by the start menu regardless of screen size?
2.
The built-in templates cannot be deleted since they're not saved the way your own custom
Presets are saved in the first place. If you open a built-in template to create a new custom preset from that, the
Delete button is more of a
"don't save this to my list of custom presets" button. You can however edit and delete your own custom presets
(the ones with the pencil symbol) that are listed on top.

In this case you can create a new custom preset by simply clicking on any of the built-in templates
(the ones with the plus symbol, e.g. Organize Movies for Plex) and then modify things from there. The
New Preset button does exactly the same, except with empty configuration. All the buttons with the plus symbol add a new custom preset to your list of custom presets.
EDIT:

The built-in templates will auto-hide if you have more than 30 custom presets. You seem to only have ~10 though, so maybe we need to consider a lower limit there to account for small monitors or high scale factors.