Yes, when adding wire we recommend soldering new wire in place for the most robust connection, the polarity (+/-) is marked on the strip light. Alternatively solderless wire clamps are available for our non-waterproof strip light.
Tinning is applying the solder to each part first. Tin the wire and then Tin the strip light copper joins , hold together and apply a small amount of heat to melt solder together to join. Doing this stops the strip light from being overheated (being quick) and the join is clean with less chance of a short being created. You can also use FLUX to help with solder pooling for a better connection and flow.
Yes, all of our strip light will handle changes in voltage due to charging etc. 12V products will handle up to 15vDC and 24V products will handle up to 29vDC. Most of our strip lighting will go into the RV and Marine industry where unregulated battery systems are the primary source of power.