Do I need to set a MX record with both my domain registrar & hosting?

Solution 1:

Should I try deleting all the records from within my hosting, so it reverts to using everything from my registrars DNS for e-mail?

I think you are mixing different stuff and hence creating confusion for yourself.

Let us go back to basics:

• your domain has ONE registrar; this is the company that registered the domain following your actions and payment for it; it could have been through a reseller, and some TLDs do not have registrars and/or allow to register directly at registry, but for the sake of simplicity let us stick to the basic idea "1 domain = 1 registrar"
• all operations on your domains have to go through your registrar as only the registrar can send commands to the registry on your behalf for your domains. Which includes things like renewing the domain or changing its nameservers
• your domain has ONE set of nameservers; those nameservers are authoritative for your domain, they contain all resource records "under" your domain. You choose the nameservers of your domain and you can change them at any time (through your registrar)
• you can choose ANY provider as your DNS provider and use its nameservers
• BUT some, if not all, registrars are ALSO DNS providers! They are separate jobs, but the same entity can do both.

So the question is not who is your registrar but who is your DNS provider. Any DNS change in the content of your zone has to be one on your DNS provider, there is nothing to do on your registrar side.

Hence there is never 2 places to go to when needing to change the MX record: you do it through the UI or API of your DNS provider. Which might be your registrar, or not at all.

Your webhosting provider is also a possible third party, it is a separate job. But it can be your registrar too and/or your DNS provider. But each job is a separate responsibility.