In a DEMUX, is it possible to route 1 input signal to multiple output signals? Say input I is routed to both output 1 and output 2. Does this scenario have anything related to data collision?
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Generally, no. The demultiplexer is a specific term and refers to a particular kind of circuit.
You do get multiple channel demultiplexers, such as 4:2. Or you could simply use multiple demux ICs, one for each output you need.
The ICs which do allow any-any connections are called crosspoint switches. They are considerably more expensive, generally, and you usually know when you need one.
When you do use multiple demuxes, or indeed, any kind of driven outputs which you tie together, you do need to be sure there is no conflict. Specifically, only one output should be driving the line at any given moment, and it's your responsibility to make sure of this. If you cannot be sure of it, at the very least you would need to add sufficient series resistance so that the current needed from/to any pin does not exceed the ICs drive strength. This will generally reduce response time and in some instances may make the the next part of your circuit not not work correctly, in case it was expecting a low impedance signal.
