All perfect praise be to Allaah, The Lord of the Worlds. I testify that there is none worthy of worship except Allaah and that Muhammad, sallallaahu ʻalayhi wa sallam, is His slave and Messenger.
The majority of the Muslim scholars have limited the defects that allow the annulment of marriage into certain types, which have been underlined in fataawa 90593 and 81422. The fact that this woman uses drugs that affect her conduct or that she suffers from depression does not oblige her to inform you of it ahead nor does it allow the annulment of the marriage unless her condition amounts to madness.
Hence, you are obliged to give her the due rights to which a woman is entitled in case of a divorce after the consummation of marriage such as the Mahr and other entitlements. If the marriage ring was part of the mahr, is considered to be part of it according to the social norms and common practice of your community, or was offered to her as a gift and she accepted it and took it into her possession, then it has become her own property. However, if you gave it to her as a loan to adorn herself with it, then she must give it back to you.
As for the plane ticket, you are not obliged to pay for it. Al-Kaasaani underlined the Hajj expenses and whether going to Hajj waives the wife's right to maintenance and whether she, while in Hajj, is entitled to provision for residence or travel in his book Badaa'I’ As-Sanaa'I’. He said:
“If the wife is entitled to maintenance according to the principles set by Abu Yoosuf, the judge grants her the right to provision for residence, not travel, because the husband is only obliged to provide for her in residence. As for the extra provision for travel such as rent and the like, she must bear these expenses and not him because she is traveling to carry out her obligatory Hajj and should bear the expenses for it. Similarly, if the wife fell sick in residence, she should bear the expenses of medication, and not the husband...” So if you did not pay for the plane ticket as a gift and intended to ask her to pay you back, then you are allowed to do so.
Allaah knows best.