Vertimas - Graikų-Anglų - F:θα στείλει το ανθοδοχείο ο Alex ή του...

Overall I like it but a couple of important corrections:

It says "ερωτικό", not "ερωτηματικό". So it should be something like "We are still intimate", or "love is in the air" if you need a similar phrase I guess. :-)

"sex thru screens" doesn't make much sense. It's cybersex plain and simple. And I wouldn't say "existed". The whole line could be translated as "We used to have cybersex"

Also I would leave full-time as is. "Permanent" sort of implies that it will continue in the future. While full-time doesn't.

So all in all:

M: We used to have cybersex...
M: We are still intimate but I started to feel down more with my own problems that didn't seem to end.
F: That there was a third person in the middle who was "full-time" with you and you ended up brawling
F: according to me, if you were feeling something true, name it passion, love, bannerdarkwinds (whatever that means), even those little everyday things would have kept you together

"brawling" is not the best word here, but I'm not sure of the meaning of "τρωγόσασταν".

Also, the last sentence isn't quite right - it should be "or did he push the situation so that you would go with him".

the sentences in English could be smoother

Επειδή φαίνεται καθαρά ότι είναι μετάφραση από μηχανή και όχι από άνθρωπο.