This user has a prior thread saying they're using win-acme, for whatever that's worth.
That seems, odd and backwards. If you give more details on this "app" and what exactly you're trying to do with it people might be able to give you better advice.
Probably not, and it wouldn't wouldn't help you as much as you think it would. I think all there is are the Scheduled Task settings. Generally, you want your renewals to be at a random time so as to spread out the load on the CA's server (as well as your own). And you want your system to check regularly to see if a certificate needs to be renewed, sometimes a CA messes something up and needs to revoke and have you ask for a replacement earlier than one might expect.
I think you might be looking for the CertificateStore.PrivateKeyExportable setting, but you're getting well beyond my Windows server knowledge.
In general, if you have actions that you need to take when a new certificate is issued, you want to set up a custom script that executes to install the new certificate and configure whatever is needed for your setup. That way, it'll just run whenever a new certificate is needed, and you won't need to worry about the exact timing.