It's very hard to find anyone who will provide free email hosting, and hosting it yourself is very involved. I recommend finding a registrar that includes email hosting as part of their competitively-priced domain registration.
Zoho — Email hosting at reasonable prices (previously started at free.)
Blacklist check — "The blacklist check will test a mail server IP address against over 100 DNS based email blacklists. (Commonly called Realtime blacklist, DNSBL or RBL)"