Is it permissible and acceptable for the questioner to give charity and communicate with a divorced woman whom he had previously fornicated with and then repented, in order to help her financially and check on her, and is it permissible to give her from Zakat?

You must immediately repent from Zina (fornication/adultery) by abandoning it, regretting it, and resolving never to return to it, while also avoiding its causes.

It is permissible to give charity to a transgressor (fasiq) or a disbeliever (kafir), but it is better to prioritize righteous people and those in greater need.

You must completely sever your relationship with the woman, because communicating with her and helping her is a gateway to temptation (fitna).

If you wish to help her, let it be indirectly to avoid temptation, such as by delivering money to her through an indirect channel, or by directing some wealthy individuals to her.

You must protect yourself (maintain chastity) through marriage, as it is a fortress against temptations.