Can I write a systematic review by myself?
There is no reason why you cannot write a review on your own, but there are at least three possible problems:


Many journals accept reviews on invitation only (but if you can find a journal that is willing to publish your review that is great).
Writing a review takes a lot more time than you think, especially if you are starting in the field and are not familiar with the literature.
You may need (or at least greatly benefit from) the experience of someone who has already published multiple papers or reviews: both to check and improve the article and to help choosing a journal to submit to.


But there is absolutely no reason not to try if you feel confident enough. Don't underestimate the time it takes though.

To answer your second question: your co-authors are usually your colleagues or people you have worked with. I doubt you will find "people to write reviews with" elsewhere.