For #1 I would say one of the following:
Next week, I can accommodate your availability.
Next week, I can accommodate your schedule.
Next week, I can work around your schedule.
The words "availability" and "schedule" can be used interchangeably in these sentences. You can also rearrange them to put the works "next week" at the end. Example: "I can accommodate your availability next week."
For # 2, I would simply say something like:
My schedule is flexible.
I can keep my schedule flexible for you.
Once again, "availability" and "schedule" can be used interchangeably here.