Will crosstalk be induced if signal running in parrallel to power trace?
Yes there will always be crosstalk. This is caused by capacitive and inductive coupling of the traces. In most cases this will however not be notable because your signal is large compared to the signal that is coupled in.

Furthermore ripple on your power supply and large dI/dt in your power trace would couse much more noise to be coupled in your signal trace than a clean power trace without ripple.

The reason crosstalk is mostly known of signal traces is because signal traces have fast changes in voltage (high dV/dt) and/or fast changes in current (high dI/dt), but depending on your application this can be the same case for your power trace.



Edit: To answer the added question:
Decoupling is one way to solve the problem of high currents trough your power traces, thereby minimising crosstalk to nearby signal traces. 

However it is not (always) good to have a higher value as decoupling capacitor. The smaller values (say 100nF) decouple higher frequencies (around 10MHz), whereas the large capacitors decouple the lower frequencies. 
For your scenarios this would mean that case 3 is in most cases worse than case 2.