When using email over VPN, can I use an alternate login and password to protect my identity when the email reaches its destination? Is the same true for Twitter and Instagram? Is it truly secure or can a technical process recover the true originator?
The goal of VPN is to protect data during transmission over some untrusted medium. Your application level data (OSI Layer 7) won't be affected by any means. Anything which could be guessed from a normal email (Twitter or Instagram) can be guessed from the same data even if it was transmitted over VPN.
Commercial VPN services are sometimes marketed as privacy preservation methods. This is not really what VPN is designed for but you can use it to hide your IP address (The company replaces your IP with its own, efficiently masking it. This is what you are paying for). It won't affect to your application data either.
The short answer is no, VPN is not designed to protect your identity. Especially not capable to hide your identity from your partner who will and should read your data. It's designed to protect your data during transmission, nothing more.
The things you’re asking about and the things you’re referencing are separate things and need to be addressed as such.
For the question of whether VPNs protect personal identity:
Yes, sort of, but not in the way you’re asking about. If you’re connect to a coffee shop wifi, for example, a person sniffing traffic on that network won’t see unencrypted data coming from you while you’re connected to the network. In the same way on the end of a social media site or email provider, so long as you are always connected to the vpn, while using said site, they will always only see your ip as the ip the VPN server has that you’re connected to.
For the question of: Can you use alternate login and password to protect identity when it reaches destination:
If by alternate login and password you mean a separate - in this case email - account, then yes that would in fact allow it to come from a separate source, but the recipient of the email will be able to see who it’s from. There are email providers out there that allow disposable email accounts to send email without the need to create an account. And to tie this back to you’re VPN, if you used one of those, while your VPN was running in theory there would be no way of knowing who the email came from. There are of course stipulations to that, but I think that’s out of the scope of this question.
Whether a VPN is truly secure, and can a technical person recover the true origin:
Well that depends on your VPN provider and ultimately the answer is no. VPN's are intended to be used to protect privacy not to provide security. But that doesn’t mean they aren’t worth something on that front. While using your VPN, if you click on a link that was meant to grab your ip address, the ip that the attacker now has is the VPN server, not yours, and although it doesn’t protect you outright there is a form of protect you have while using it. Can a technical person recover the true origin, maybe if they have the right resources.
Whether an anonymous account is truly secure, and can a technical person recover the true origin:
Actually yes, well it could be, given that the account hadn’t contacted any other identifiable account or information including your ip address, you would have a good chance of the person not discovering who really made the account, not even the site would know.