Does "to eat" (äter) have to be conjugated?
There are none in the present tense. They don't change according to person, they do change according to tense though.
Yes, I saw. I was going to reply but I figured that you might check the feed again. I don't know why it was down voted either.
"Äta" is actually supposed to be tricky :), since it is irregular:
jag äter - jag åt - jag har ätit
I eat - I ate - I have eaten