Yeah, it’s an adverb. The comparative and superlative are hellre (rather) and helst (’most of all’). There are no 1:1 English translations of these except for the comparative.
How about I would happily take a little more coffee, compared to the gladly which seems to be acceptable?
gärna (comparative hellre, superlative helst) gärna both means ''willingly, gladly, readily'' and ''easily; which easily or readily happens''
Could I say "Jag åt gärna glassen." if I were to mean I ate the ice cream with pleasure/enjoying it. Or can this structure not be used with past tense?
You can say it, but the meaning is more like "I was happy to eat the ice cream."
I would like to take some more coffee is something I could want to state when I am pouring myself a tiny bit of coffee in order to share equally with the others present. I would love to have some more coffee is something I would use if someone else is pouring the coffee. I think both can be fine translations for the Swedish sentence.
I've definitely heard "take some coffee" in former British colonies, but never in America I guess