Do 12V and 24V strip lights work together?

No. A 12v LED strip won't light up if a 24v LED strip is connected to your project. RGB LED tape may show faint red glow if connected together; 12v strips connected to 24V power sources become even more dangerous due to overheating within seconds, potentially even leading to fire hazards if left connected for too long.

Does 12V strip have a higher safety rating than 24V strip?

Both ratings are relatively low voltage ratings and thus differ little in their safety rating. As previously discussed, voltage drop can play an important role - lower voltage systems result in more losses; it's more likely you'll experience voltage drops with 12-volt systems.

Can a LED strip 24V work on 12V voltage?

A transformer or voltage boost may be necessary to connect a 24-volt strip to 12-volt power source, as 24V strips consist of multiple strings of 6 LEDs which cannot be dismantled in order to fit with 12V sources.

Can a 12V LED strip work on 24V?

Unfortunately not, as overvoltage will damage and destroy a 12V strip when powered with 24V power source.

Which LED strip design is better: 12V or 24V?

This depends entirely on your application; now that you understand both its advantages and disadvantages. 24Vs may be suitable if cut length doesn't matter; 12Vs would be more advisable due to space restrictions.