Sentence #1, to me, cannot take an -ing form: intends to see.
#2 and #3 are gerunds, as you can see by recasting them:
2-- Applying for the job immediately was his advice.
3-- Spending so much money on clothes today is what she regrets.
#4 is a participle as part of the continuous verb (just remove the adverb to see this):
4 My wife is shopping now.