Is there any possibility of reconciliation after divorcing the wife three times? And how many divorces have been enacted, given that the first divorce occurred after a disagreement over the place of birth, the second divorce occurred via a text message, and the third divorce followed a lawsuit for harm-based divorce?

If you took back your wife after the first divorce (ṭalāq) before her waiting period (ʿiddah) ended due to pregnancy, she has returned to your marital bond (ʿiṣmah), and it counts as one divorce. As for the second divorce that you wrote in a message, it is effective if you intended divorce by it. Your taking her back (rajʿah) in writing after that is valid if it was during the waiting period and you intended to take her back.

If this taking back (rajʿah) was valid and no divorce occurred after it, then your wife is within your marital bond, and two divorces have been counted against you. However, if the taking back was not valid and the waiting period ended, then your wife has become irrevocably separated (bāʾinat) from you, and she is not lawful for you except with a new marriage contract.

Your filing a lawsuit for divorce due to harm does not effect a divorce merely by itself, unless you pronounced the divorce or wrote it with the intention of effecting it. In that case, you would have divorced her three times, and she would be irrevocably separated from you with a major separation (baynūnah kubrā).

Deception and trickery towards the court are not permissible. Regarding your wife's request for a separate dwelling, if you stipulated in the marriage contract that she would live with your sister, then some scholars are of the view that she does not have the right to demand a separate dwelling.