There are a few options, and they are free. First, google hangouts and google classroom are fine for this. If you want, you can just use drawing in a google doc or something for the pictures.
If you want a little higher level functionality, you can checkout some kind of courseware like Moodle, Blackboard, or Canvas which will let you do things for free but isn't immediately obvious for students.
Finally, I would highly recommend CoCalc.com . Here, you can use a variety of computing languages and tools but there are also very nice chatting capabilities including video conferences. I tend to use Jupyter notebooks a lot with my classes, so I can pop one here and have a conference with students online including a video chat, but they can also always drop me a note in the chat and I'll be able to see this even if we're not chatting live (this is what you see on right side of screen). Also you can use a
sagechat and have a classwide document for chatting. All will let you write mathematics with $\LaTeX$.
Last, you may want to checkout etherpads (etherpad.org).