1. Ideally, backup solutions does have an option to directly restore to a ESXi host in such scenarios. Please check for such options in backup application
2. Post restore, these VMs which were removed earlier might come back to inventory as they are stored in vCenter database. They might be listed as invalid as you have already removed the files, so a manual removal from inventory might be required.
What backup vendors recommends you as a technique to restore vCenter Server is to add an ESXi host as standalone and recover it there. Most of the backup solutions let you do that as they can also consume ESXi by their APIs.
About your 2. Questions
No, your changes arent lost when vCenter comes back again. The vpxd will receive the current state of the ESXi trough the vpxa agent on the host. Its similar as when you choose within the trouble shooting option the Restart Management.