is "Jag köper gärna en ny lampa till dig." also an accepted option? is there any difference between "till" and "åt" in this context? (e.g. "Jag köper leksaker till barnen.")
Yes, it's an accepted answer when translating from English into Swedish. In this context, the difference between åt and till is minimal. (it's possible, but not necessary, for åt to have the implication 'so you don't have to').
i have a question about indirect objects, the "you" here. Where can it go in the sentence? Here I see that it is written out as "for you", but when I tried to put it in just as "dig" where it would go in English (right after the verb), that got marked as wrong. Does Swedish even HAVE indirect objects, or is it always written out as part of a prepositional phrase?
It would probably sound better to say something like "I will buy you a new lamp with pleasure" or "I will gladly buy a new lamp for you". (In English you give something to someone but buy something for someone).
It is common in Swedish to use the present tense with a future meaning and in many situations, it is most natural to translate this with a future tense in English.
I notice there's a variation of this comment on each exercise with an adverb. I call it an aside. It's almost a parenthetical. You have to frame it with commas if you are going to insert it in the middle of the sentence like that. I would not use that word-order unless the Swedish you are translating also has an aside. "I will gladly buy it for you." is the basic placement which needs no commas. "I will buy it, gladly, for you." has the aside. "I will buy it for you, gladly." might be an afterthought placement. Placing a manner-adverb at the beginning like: "Gladly, I will buy it for you" almost always is an answer to a question better reflected by making the adverb it's own sentence; instead it can be used for a strange vocative effect or an emphasized imperative effect like "Gladly, you will obey".
So, I'm saying word-order matters. I mostly don't know how to do these things in Swedish but I aim for the simple structure in the answer if I think it's the simple structure in the question.
Since gärna is an adverb, I prefer to translate it to "gladly". Maybe the prepositional phrase in Swedish is "med glädje"?
What are the other answers that would be accepted aside from "love to"? "Willingly," "gladly," "readily"?
How is "g?ärna" conditional? I wrote "I am happily buying a new lamp for you"--which was wrong. I purposely avoided making it conditional as I didn't see any clues that there was a conditional form...?
"I would buy with pleasure a new lamp for you." wasn't accepted. I know this is an unusual construct but it is grammatically correct. I am a native English speaker, by the way.
While it may be "grammatically" correct, if I heard someone say that I'd immediately think the speaker's native language was not English. When my Spanish speaking students say, "I am reading the book of my brother," I encourage them to say "My brother's book" instead, even though their sentence is technically grammatically correct and in unusual circumstances might be used by a native.