1) Since my site now is accessed through HTTPS, does that mean that any information going out of my website is encrypted?
Yes. You have a certificate that is used for the encryption. The only thing a self-signed certificate does not provide is the certainty that you are who you say you are. Anyone can generate a certificate, but the signing authorities require some proof of identity.
2) What is Stunnel? Do I need to install it too?
Search engines are your friends. But don't confuse SSL and SSH. They are two completely separate things.
3) What is OpenSSL? Do I need to install it?
You probably already have. Otherwise, how did you generate your certificate?
If you order a signed certificate and get it in some unknown one-OS-only format, you will probably need OpenSSL to convert it to something useful. The Abyss must come with some SSL implementation to do HTTPS traffic. This may or may not be done with OpenSSL internally, I don't know.