If you figured this all out on (mostly) your own, then I'm impressed. You wrote down most of the principal techniques and theories that we use on the suicide hotline.
However, our bread-and-butter technique is tentative statements: "It sounds like you're upset because..." or "It seems like you feel betrayed when..." As you can see, tentative statements are where you sum up what the person's been saying, reflect their emotion(s) back at them, and make them acknowledge it. It's tentative, so it's easier for them to accept or deny it (in theory, I had a case last night where he still felt like I was telling him how he felt).
It took me a long time to realize how to show empathy. Empathy is so easy and natural, but if I say, "I understand," I'm showing only sympathy; sympathy is worthless to a distressed person. So, I had to work on showing empathy through tentative statements. Often, after I reflect a person's emotions back at them in one statement, they pause for a minute as if that's what they wanted all along.
I like to think of counseling as a mirror with a different angle; it allows a person to see themselves from a different perspective. Also, counselors, for me, have been great for coming up with ideas to overcome problems because they have more experience.
Speaking of coming up with ideas, you should always present suggestions as questions, preferably as questions like, "Well, have you tried doing..." or "What about doing...". When you present them as questions, the person will hopefully think about it before accepting it. If they do accept it, they usually feel like it's their own idea, which helps them stick to it.
Something that seems to help people a lot, especially if they're in distress and unable to sleep at 2am, is focusing on the next day. "After you hang up, what are you going to do?" "You're unemployed now, so what are you going to do in the morning?" Regardless of the time, I like to end the conversation by asking them their plan of action because focusing on the future often makes them feel better. Also, those questions are great for trying to close a cyclical 2-hour call.
Finally, remember that it is impossible for one person to know exactly how another person feels. Even if they describe the situation well, and I empathize as much as possible, I still will never know exactly how they feel.