The "Improved Critical" and "Superior Critical" ability attack rolls of 18 and 19 don't trigger the crit roll for damage.

Also, my level 7 Fighter with "Magic Initiate" that's learned "Ray Of Frost" rolls 2d8 for damage (which will probably scale with level), but should stay at level 1 damage of 1d8.

Quote from evilplans >>

The "Improved Critical" and "Superior Critical" ability attack rolls of 18 and 19 don't trigger the crit roll for damage.

Also, my level 7 Fighter with "Magic Initiate" that's learned "Ray Of Frost" rolls 2d8 for damage (which will probably scale with level), but should stay at level 1 damage of 1d8.

Cantrips like ray of frost scale with character level, that’s a universal rule acting correctly.

As for the other thing, their system can’t do that yet. I know it’s only been 8 years since the book came out, but their system can’t do that yet.

I see what you're saying, but "Magic Initiate" only let's the Fighter learn the level 1 of a spell.  It shouldn't go higher in this case. No?

Though, I'm new, so I'm still learning.

Cantrips don’t have “levels,” they just automatically improve as you gain character levels. That feat allows you to learn 2 cantrips, and one 1st-level spell. That 1st-level spell will always be cast at 1st-level, but the cantrips will automatically improve as you level up.

Ohhhhhh got it!  That definitely clears it up. Definitely lots to learn and appreciate these sorts of mechanics.  Thanks so much! 

Happy to help.