Heads up, "I've" is not grammatically correct when "have" is your verb. Using "have" in a contraction when you're using past-perfect tense. For example, "I've been" is an acceptable shortening of "I have been".
Is it actually incorrect? I don't think it's necessarily wrong, but it just sounds bizarre or Shakespearean if you use it when it's not an auxiliary verb.
"I've no need for that." is a perfectly cromulent sentence.
Yeah, not "incorrect," just non-standard. The yardstick is: did your interpretation match the intended one? Clearly, he was able to get there so it's firmly in "acceptable use." Any further whinging about grammar is likely to just be construed as gatekeeping.
As a native BrE speaker I’d say “I’ve X installed” is a little weird, fine in speech but written down it doesn't look right. “I’ve installed X” is fine.
The yardstick is: did your interpretation match the intended one?
I think that's just you. There's a few examples of rules in English that aren't required to get a point across, but sentences that break them sound grating. One such example is adjective order