Gramma mamma here. Your first sentence is right, and this is the rule: Certain conjunctions used to talk about future time - after, before, when, if, unless, as soon as - are always followed by a present tense. They can be followed by a present simple tense: 'I'll tell you about it when I SEE you' or a present perfect tense: 'I'll tell you about it when I'VE READ the report. So the sample sentence 'I'll be lonely after you've gone' is absolutely correct. It would be wrong to use a future simple or a future perfect following 'after'. You cannot follow 'after' with 'will'. The second sentence is wrong, because the sequence of tenses makes no sense. If it was a native speaker who wrote this it was probably a typo. If he/she was talking about the past, it should be either "I did update the project after I talked to you". "I did update the project after I'd talked to you". The same sentence in the future would be this: "I'll update the project after I've talked to you". I hope that helps. Please ask if anything's not clear.

I think you can, but I find it rare. The first example you give is OK, but the second should be just "after I talked to you", because the next action (updating the project) is already in the past.

The first sentence isn't present perfect...it's future perfect: "I will be lonely after you [will] have gone"...it's an interesting point you've raised, I've never thought about how the "will" can be ommitted in the future perfect. But it's not a very common verb tense, so not an issue to get too worried about. Just don't get confused: this isn't present perfect. However it looks a little strange to me, as the future perfect is usually used to contrast a future (will have + PP) with an EARLIER future (will + inf), however that sentences switches the times around...so it looks slightly weird The second sentence looks much weirder to me, actually I think it's downright wrong. That's not to disrespect your NY friend, keep in mind that native speakers make mistakes all the time, sometimes speaking, but also in writing too. Just typing errors, nothing to do with their English language being bad or anything.