"My younger sister also wants iced tea."
Yes. The web notes teach this. Report it as 的 may be omitted or the notes need to be updated.
yup, report it. it's more casual without the "de", but more formal with it
In the right context, you can drop the 我 as well as the 的; e.g., if there is no one else's younger sister there, I think you could say 妹妹也要冰茶。
From what I read (after googling 想 vs 要), it seems 想 is more in line with a conditional form of want (but can be used to be polite), while 要 is more indicative form. Though, I would like to see if a native/fluent speaker could confirm this or not. My teacher always told me to use 想, but never really explained why (not enough time in three months).
It‘s lots of intuition I feel like. I put in "想喝冰茶” which pretty much corresponds perfectly to the concept of "I want ice tea". We just omit the verb, still, "I'll have a beer" implies I'll be drinking it in 99% of all cases.
To me, 想 is more an expression of want or desire (or even longing, pining, or missing, as in 我很想你 / I miss you); whereas, 要 is more an expression of intention:
我想 ... = I would like ... (or "I want ...") 我要 ... = I'm going to (have) ... (or "I will have ..." or "I'll get ..." or "I will order a ...")
I would generally prefer to use 想, but maybe I would be wrong to do so, and I certainly would not think 要 is wrong here, either.