Remember that “caru” is a verbnoun, which sort of equates to either the “ing” form in English (loving) or the infinitive (to love). Love, as a noun, is a different word.
It’s “Dw i’n’” and not “Dw i” when you’re joining bod (“to be” - am, is, are, etc) to a verbnoun, noun or adjective:
Dw i’n caru - I love / I am loving (verbnoun)
Dw i’n hoffi - I like / I am liking (verbnoun)
Dw i’n oer - I am cold (adjective)
I wouldn’t worry too much about it. As you carry on through the course you’ll just learn when to use what.