What do they ask? How do they stop you bickering? How do you know it is helping? How do you know it is time to stop going?
They tend to ask leading questions. They try and get YOU to come to the solution yourself, which teaches you to think differently in situations.
They can't stop you bickering because they can't control you. YOU stop you bickering. You need to make a conscious effort to stop and deal with things a different way. Whether it's writing down your grievances (journal or write/burn), or walking away for a certain period, or counting to 10. They try and help you find a different way to cope with your need to bicker but if you don't put that plan in motion, of course you still bicker.
Knowing whether it's working is developing certain goals and your personal situation. If your goal is to bicker less, then bickering less could be seen as "it's working" however if you're actively not bickering only because you're in therapy then it's not working. So it's more of a long term goal of finding out WHY you bicker, finding different ways to stop it and to cope with disagreements.
Knowing when to stop going is also a personal thing. In my experience the visits become less frequent. It doesn't hurt to go again from time once you're "better", especially individually, to get a gauge on how you're feeling etc. As someone said above, most people leave it really late so it's a hard slog back, a relationship takes work and sometimes you need people to help with it.
I feel weird that it is sharing personal stuff without getting to know them because they are a professional and not a friend.
This is exactly why people go to therapy. Friends are great, but most people don't tell their friends the entire truth (whether it's fear of looking bad, or fear of being told your wrong) and most peoples friends tell them what they think they want to hear. Friends are typically there to support you and that's not always helpful. Sometimes you need to be told you're wrong.
A therapist is there to help you, not judge you. They have no vested interest in you like a friend does. A therapist is a good outlet for the things you want to talk about but don't want to mention to friends (for example: when you're worried you've been harping on about the same thing and that they'll stop caring/listening) and for you to be completely honest without fear of reprisals.
How do they stop you digging a bigger hole for your relationship?
They can't stop you from doing anything. You are still a person with choices. What the aim is though, is to find better ways to deal with situations, better coping strategies.
How to deal with things in a relationship also depends on your partner.
In my particular case, I'm a "bottler". I stew on things and get more and more upset which just results in me being more upset about something than I would have been if I just said "I don't like when you X" or "I'm upset because Y" and then let it go. I recognize this in myself and strive every day to change it (at least with my DH, there are some who wouldn't react well to my actual feelings on a situation).
I went to therapy when I was 19/20 after I had a breakdown (so about 13 years ago). The first therapist wasn't the best, but she did teach me something that I still think about to this day, and it's about how to recognise when I'm having irrational thoughts (which is a sign of depression - for me at least) which she called "definites". So when I start thinking things like "<span class="underline">everyone</span> hates me" and "I <span class="underline">always</span> get let down by people" (among other things) I know I'm thinking irrational thoughts. I know to talk myself around "well no, not everyone. You have friends like X, and Y, and your family Z and A" etc etc. Basically stop myself wallowing.
Therapists aren't miracle workers, but if you go in with an open mind, and willing to change and listen, then I think it will help. Maybe not always in the way that you think you need though.