issue #1: I would tell them what day you can cut. They can take it or leave it.
The ones that will not commit are taking you for a ride. The most likely want to hold out till the grass is a foot high and want it cut for a weekly price. When they do this show up and tell them since the lawn has been so neglected you will have to charge $XX (2-3 times weekly rate) because of extra time and wear and tare on equipment
Issue #2: I would charge a higher rate because of not being a seasonal customer. I would take them only if I have time in my schedule.