See you on 7th October or I am seeing you on 7th October

I am about to say goodbye to a friend that I know that I’m going to meet again on the 7th of October.

Before leaving should I say “See you on the 7th of October", "I will see you on the 7th of October” or “I am seeing you on the 7th of October”? My doubt is, if it is a fixed plan, why not use the present continuous form, I am seeing you..?

And in case I am looking at my schedule and someone asks me when I am going to see someone (for example my mother), can I say, "I am seeing my mother on the 7th of October"?

Since you will be seeing your friend on the 7th of October, you could say

See you ... / I will see you ... / Can't wait to see you ...

• soon.
• next month.
• on the 7th of October.
• in a couple of a weeks.
• in a few weeks.

As for someone asking you when you are going to see someone, you could say

I will be seeing my mother on the the 7th of October.

You can replace the on the 7th of October with any of the five options above.