I think you'll find that trying to run OUTGOING mail from your server will be a continuous exercise in frustration
Before I started bouncing around the planet and decided to have my domain hosted, I was doing this, and ran into all the problems you described; mail being banned because of RBL's for netblocks of DSL/Cable Modem networks, the whole nine yards. Very frustrating. But one system will accept your mail from the network you're on, that being your ISP's mail server.
Now, I can't couch for every ISP, but I was on a large cable service providers network, and their servers (at least at the time) didn't care that they were relaying mail from mydomain.com, off to where ever it was destined. I was also fortunate in that they weren't blocking port 25 inbound, which some do as well, to dissuade people from hosting mail servers on their home computer, and cut down on spam.
Probably, when you signed at the installation of your service, you agreed NOT to run a server on your connection either. If you do so, and set it up very carefully to not be an open relay, etc. they may leave you alone. I got away with it for three years, while others I knew at work, on the same providers service, had set up servers in a neglectful manner, and they didn't make it a few months before they were on them to shut it down or have their service shut down... Lesson there seems to be that at least _some_ providers will turn a blind eye to a properly configured system...
You could try, but nothing is definite, and the provider of course can change the game, at any time, and put new road blocks in place without warning to you, because of the nature of the service agreement. And honestly, some places hosting your site and mail for barely more than $5 a month, it's hardly worth the hassle, although it can be quite a fun learning experience if you are patient.
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