Fascinating profile name and profile picture! xD
How does "ikaga" translate here?
Literally it is How.
It would be better to understand the whole block いかがですか？as an even more polite form of どうですか?.
Why does 欲しい not work?
It is grammatically alright, but socially unacceptable to speak about your counterparty's desire.
あまいくだものをどうぞ should be accepted
I see what you're saying, but I think the nuance is different. いかがですか is asking you a question. You can say yes or no. If someone says どうぞ, they're not asking you a question. They expect you to take what they're offering.
What about あまいフルーツはいかがですか？
フルーツ (furuutsu) is used a lot in daily Japanese life in my opinion. It's good to learn 果物 (kudamono), but フルーツ is just as valid an answer.
I think it's pretty weird to say "fruits". It's not wrong, but we usually say "fruit" in naturally spoken English because we treat "fruit" as uncountable.
沢山ありますよ。例として いくつか の オレンジ、レモン と グレープフルーツ!
I thought that this sentence would mean, "How are the sweet fruits?" I thought that was the meaning of いかが, and that's what Duo taught me.
That's a valid interpretation. いかが and どう are commonly used to offer something to someone ("would you like ~?") but can also be used to ask how something is.
Can anyone tell me why あまいくだものはほしいますか is wrong? I would have thought you'd use ほしい to talk about wants
I've never seen a verb such as ほしいます exist, maybe you meant ほしいですか？since ほしい is an "i" adjective...
To add on, saying ほしいですか (hoshii desu ka) literally means “do you want it?” and would not be used to offer someone something.
いかがですか is definitely the way to offer someone something yeah, and not ほしいですか