What is the ruling on the money that must be paid to my ex-wife after being in seclusion with her, and is it permissible to donate it as charity on her behalf if paying it would lead to فساد (corruption/harmful consequences), and what is the ruling on my false testimony that no seclusion took place?

The dowry (Sadaq) is the obligatory compensation due to the woman from the man in return for intimacy. It becomes fully due by one of four things: private seclusion (khalwa (definition)), sexual intercourse (jima'), death, or foreplay (mubasharah). If there was private seclusion, foreplay, and intimacy with your wife, then the full dowry is due to her, which is what was agreed upon from the furniture list and the wedding gifts (shabaka). However, if the divorce occurred with an agreement to absolve you from part of the dowry, then you are only obligated to what you both agreed upon.

As for your testimony that the dowry was not determined due to lack of private seclusion and consummation, this is a false statement and a major sin (kabeera), requiring immediate repentance to Allah. However, you should not disclose this matter now, as it may cause damage to the woman's life. You must feel remorse and increase good deeds to expiate the sin.