What is the ruling on my continuing to try to invite members of a British Muslim forum to adhere to Islam, knowing that they do not respond to my invitation, and is my pretending to be a young man in this forum considered playing with girls' feelings?

May Allah reward your eagerness for righteousness and your efforts in da'wah. Impersonating someone of a different gender or using a false name is a form of lying that is not justified by calling to Allah. Therefore, this impersonation must be rectified by withdrawing from the group or by correcting the name, then choosing a legitimate means for da'wah.