Opening multiple concurrent ssh sessions from different clients but with the same user/password. Is that possible?
Yes. This is the default setup in every *nix distribution I've ever used.
It wouldn't be rare to have 15+ ssh sessions from different hosts all with the same username/password.
Yes absolutely. Just like you can open up multiple terminals on a local host, so you can open up as many remote terminals as you could have use for under the same user. It's actually quite common ... right now I am SSH'ed into one server from at least three machines sitting on my desk and one more that I left open in another place.
If you do a lot of giving specific credentials to people you might find it worth learning key based authentication. If you give a bunch of people the password to a a shared account then need to revoke access to one person, it's a nightmare. You have to change it for everybody. If you use key based authentication, each person can have their own key (with their own passphrase protection if they like) and you can add all the public keys on the user account. When you need to revoke someone just drop that person's key without affecting anybody else.