I don't really get this. Where do you draw the line between disposable and non-disposable email? What prevents anyone from creating <random string>@gmail.com addresses?
Seems to me that 1) Gmail accounts aren't that hard to farm 2) most spam comes from free webmail providers not disposable email and 3) a captcha will solve most of your problems and if it doesn't, it means your site is being specifically targeted by someone with cash to burn, so you can assume that they'll have emails that aren't on the blacklist. At that point, invest in detection and moderation.
This is 100% not true. Yes, the main site will require it, but there are legacy "portals" that allow signup without a phone number. No, I won't link to said portal.
As of gmail -- one of the guidelines for the list addition is whether you need to go through some sort of a registration. If you do then it is usually not treated as disposable by us.