On this point, US law isn't concerned with acceptance by a foreign country, it is only concerned with US law – under US law, are the couple divorced. When they are, the F2 visa holder is then out of status. Whether or not they should then leave the US is a complex personal question. They are not legally required to leave, as long as they adjust their status. When (assuming) they file their I-751 petition, they can ask for a waiver of the joint filing requirement. There is a chance that they will be denied the waiver if USCIS feels that the marriage was a sham marriage (which could be supported by the F1-holding spouses allegations in the divorce proceeding).
Assuming the couple are not yet divorced and the F2 spouse wants to marry a US citizen, they would need to first get a divorce. The usual pattern for divorce laws is that you must be a resident of the jurisdiction to get a divorce in that jurisdiction, and that jurisdiction gets to set its own rules for residency. Currently, Nevada requires 6 weeks residency by a party in order to file for divorce, but there is a meme that some decades ago, simple presence in Nevada was sufficient. As far as I know, no jurisdiction allows divorce proceedings to be filed by parties who are not present in that jurisdiction (which then implies "Yes, in the US").