Only you will know the answer to this. I would suggest working on yourself first though... Depression is very treatable. Get the help you need. It will help you if you ever decide to marry again. Happiness is always better if you have someone to share it with.
Best to work on breaking the depression. It might make it harder to meet the right person. Depression can hold us back and if it does, we tend to pick the wrong people and that makes things worse. You are pretty young. Take a little time to work on feeling stronger in your own world. Once you have, finding a good guy will be much easier. Until then, your own judgment could be off.
Only if you find the right guy, and you do that by dating around and enjoying your freedom. Don't go looking for a future hubby, just find a date, then another date with another guy, just have fun, before you know it one of these guys will stand out from the rest.
Don't rule it out but don't make it an obsession like it's something you have to do to be "normal". You can have a really nice life as a single or an equally nice life if you find someone with whom you truly love and want to share your life with.
Yes you must even if you had kids you must remarry. It is legal. All birds find shelter during a rain. But Eagle avoids rain by flying above the clouds. Problems are common but attitude makes the difference Dr.A.P.J. ABDUL KALAM. (ex president of India) So change your attitude and do whatever your sweet heart permits. The world is beautiful, it needs your smile.