Prospective PhD advisor encourages me to apply and positively mentions relevant experiences. What are my success chances? I had recently e-mailed a professor asking for opportunities in his lab. He responded as follows -
Email content:

Dear [redacted]
Thanks for your interest in my lab. My lab is planning to hire multiple Ph.D. students who will start in the fall of 2021, and the application window is going to be this Winter.
It's good that you have some relevant research experiences, and I encourage you to apply to my lab at [redacted]. When you submit your application to the department, please mention my name in your personal statement. Also, please let me know when you submit the application.
Best,
[redacted]

Can I take this as a positive response? Does that mean he will take me in if I apply? How do I respond back to him?
The professor's asking to be kept informed, which is certainly a positive sign because he's interested enough to want to know what you're doing. At the very least he's not outright rejecting you.
On the other hand, there is no guarantee he will take you on until you actually receive the offer letter.
I don't think there's much more to say other than thank him, reaffirm that you will submit an application (if you are planning to do so) and say you will keep him informed when you do.