A trigger is a type of sensor that pulses once a certain threshold has been reached. It doesn't really matter - you can interpret pulses from a trigger as just input anyway.
Take the motion trigger for example. When there is no movement, the signal is a constant LOW. When there is motion, a HIGH pulse will signal that. You can interpret the frequency of pulses, and the duration of the stream of pulses as how much motion there is. This value can certainly be a scalar.
Sound can be interpreted in a couple ways. The sound trigger can send a signal when the level reaches a certain intensity. Again, interpret this in any way that makes sense to the logic of your project. Sound can also be interpreted as a continuously varying level. This is what the microphone bit does. So depending on how you are interpreting the data, your choice of input source will vary.
Instead of splits to combine your data sources, use the logic bits: double and, double or, nand, nor. Splits take a single input and have two outputs! The logic bits take two inputs and have a single output, which is what you want when combining inputs.
Even better would be to use four of the analog inputs of the arduino bit, and treat each input independently, and outputting the calculated result. Although the Arduino has limited input connectors, three more are hidden on the solder-holes in between the A0 and A1 connectors.
This will give you the ability to monitor light, heat, sound and motion. The arduino will monitor all four, and signal the cloud bit when your conditions are met. While it is possible to monitor, and transmit an analog signal using the cloud bit alone, you will need to have a different cloud bit for each sensor. Combining the inputs with external electronics - either an array of logic bits, or a microprocessor (the arduino bit) is much more versatile. And economical!