A listserver is indeed a program that typically runs on the same program as a mail server. It can provide facilities for users to subscribe and unsubscribe and much more. Your ISP may just provide a basic mailing list facility and that may be sufficient for your purposes. It would be the most successful method of mass-mailing anyway. Your ISP is going to accept its own mail, whereas it may not accept a mass mailing from a server that you yourself are running.
Re 1: it is possible that after this previous mailing, you or your ISP became blacklisted, and that accounts for subsequent problems.
Re 2: yes, certainly. Your ISP should be able to do this. Alternatively, it may provide black/whitelist controls, but they vary so much you'll need to check that out with your ISP.
Outlook can certainly filter out this kind of spam (look up filters in the online help) but better to get it done at the server end. That saves bandwidth.