Grannie2:
I'll answer your questions in the order they were given.
1) No, but I did with one just like them
2) I don't know
3) Yes, I have
4) The definitions of both, with slight variances, point to vanity publishing
5) Based on my personal experience, I'd suggest that you find a literary agent. The internet abounds with agency contact sites. Your only cost will be the stamps that you put on your query letter and SASE, or at the most, these plus printing and mailing costs for your query, title page, synopsis and sample chapters (If the agency submission policy asks for these items).
6) An agent will reject your work if they deem it unsuitable, hence the SASE (self addressed stamped envelope). This makes it very convenient for them to reject you. Sounds brutal, and it is. The vast majority of queries are rejected. If your query and other work is good enough, an agency will ask for the entire manuscript. If the manuscript is acceptable, the agency will offer you a contract. Then they'll submit your work to publishers, and if the work suits the publisher, and it's good enough, you're on your way.
If you're serious about your writing, avoid vanity publishers at all costs. Believe me, I know. I've been down that road. Remember that commercial publishers don't advertise - - they don't have to. When your work is good enough, an agency will pick you up. Just getting to that point requires a lot of work, and usually a lot of rejection. It's a great feeling when you finally land an agency to represent your writing.
And do yourself a big favor - - toss the vanity letter in the trash.
Best of luck to you!