Yes, tape lights are dimmable. Most tape lights have a DC electrical signal that allows the brightness to be adjusted. Verify your tape light is dimmable by checking the specifications on the label. The Spec Eco Tape Lights in this series have dimming capabilities with most ELV and TRIAC dimmers.
HomElectrical provides American Lighting Tape lights that have different dimming qualities. These are perfect for your home and other places.
Whether or not the tape light can be cut depends on the brand product. Tape lights will either have a cut line or not to let you know if it can be cut. For example, Spec Series Tape Lights have cut lines at every 2.8 inches with a 16.4 ft max run.
If it does have a line, make sure to be precise while cutting the light. It can be challenging to reconnect the lights once they are cut. If you do not cut it correctly, it could lead to waste as well as using additional connectors to help connect the light.