The first picture displays that I have only one feature branch on VSTS:
The second picture displays that I have develop and master branches as well in visual studio locally:
There were master and develop branches on remote before, but seems to disappear suddenly. My commit history does not show any clue of them being merged into the feature, How do i find out what has happened? I want to avoid merge conflicts
According to your description, someone/others may deleted the branch in server side. VSTS will not auto delete your branch.
You could double check this through search option, enter your branch name here such as develop.
If the branch status is deleted ,you could select the ... option and choose recover the branch, finally sync local changes with server repo.
Another possibility, you have selected the wrong remote repo. You may pushed the branch to another repo than the one you selected now.