Can my web server be at one hosting company, and my email hosted by a 3rd party?
Yes. To do this, you will need access to the DNS records for your domain. The MX record allows you to set up a mail server that's separate from the web server.
Google offers a service that will manage your domain's email through GMail, and the instructions on how to reconfigure your DNS for this service can be found here.
Yes, this is possible. You need to use the combination of "A" record and "MX" record.
- "A" record will point to your web server where your application is hosted.
- "MX" record will point to the server where you want to host your email.
A complete step-by-step reference on how to do this can be found here Hosting website and emails on different servers
It is possible no matter where they are located, as long as you have control of your DNS records. I have run many sites where the web server is located in our building and the mail server is at the customer's own site, connected with via an unrelated ISP. In one case the web server is in the USA, and the mail server is in the UK.
The DNS records can be on a different server again. Some registrars include editing DNS records in their interface, others just let you set the DNS to another server.
The records that determine the e-mail server are called MX records. They take the name of the mail server (not it's IP address). The records that turn names to IP addresses are called A records - you use these for "www" etc.