I use glasses at night and put on contacts in the morning. But my prescription for glasses is a lot lower. Is this okay?

Yes. Once you get beyond a certain eye power, the numbers for glasses versus contact lens power will change to obtain the same level of vision. For example, if you wear -4.00 in glasses, you're contact lens power will likely be -3.75. Conversely, if you wear a +4.00 eyeglass, your contact lens power will likely be +4.25. Any astigmatism number may also be different.
Lens effectivity. You are describing physics. Specifically optics. The optical principle of lens effectivity states that as you move any lens away from the eye it becomes more positive. So if you wear glasses prescription +7.00 then moving them closer to eye makes them less positive, so to offset this the prescription must be increased to offset. The amount change is determined by distance moved.
Absolutely. It turns out that the prescription of a lens changes the closer it is to the center of the eye. So, contact lenses and glasses often differ in their prescriptions. This difference becomes even greater with larger prescriptions. As long as you do not feel any strain with either glasses or contacts, you do not need to worry.