Oddly enough, 1 is okay (but informal) but 3 is not. I'm trying to figure out why.
"You can come if you want" is very common. "He can come if he wants" is also okay. Both are quite informal. "I proposed that she go with us..." is much more formal, but I don't think that's the main problem with sentence #3. I whink using "want' without the "to" just doesn
I edited my above: My conclusion is that "want to" is phrasal, and that you can only exclude the "to" if you use the common phrase "if you want". This expression can't be used in the negative.
Other sentences that don't work:
...If you don't want. Do you want? I do want. etc.