Hi Emezim, and welcome to AF
Sorry to hear about these problems. I can only guess that you'd stored the contacts as belonging to that GMail account, so removing the account removed the data associated with it, including the contacts. I'm surprised that you couldn't just restore them by re-adding the account though.
It is possible to set up contacts to be phone only, in which case they'd not depend on any account. You need to select contact type "phone" when adding the contact. The default contact type will be "google", so you would need to spot this and change it.
I'm afraid I know nothing about Hotmail, and actually don't use the built-in email client, as I was using a 3rd party email app with my previous phone and saw no need to switch. Hopefully someone can advise on that.