Distinguishing FIR and IIR from difference equation
Welcome to DSP! First of all I would recommend reading chapter 2, specially 2.2 to 2.5 of Discrete Time Signal Processing 3rd edition by Oppenheim and Schafer. Then 3.2 and 5.2 of that very same book.

About your question. Well, in general (see comments on Axel answer for an exception) if you see an equation which depends on past output terms, like $1.2*y [n−1] $ in your equation then it is an IIR system. If it only depends on current, past or future inputs, it is an FIR system.

If it is an FIR system, you may determine stability, causality, linearity and time invariance from the Linear Constant Coefficient Difference Equation. However, if it is an IIR system, unless initial conditions are given to you, there's no way you could prove any of these because you don't know the value of the past output the first time you are going to "use" the system and it could determine whether it behaves one way or another. 

For a system for which the input and output satisfy a linear constant coefficient difference equation, if the initial condition is that the system is initially at rest, then the system will be linear, time invariant, and causal. For stability analyze the Region of Convergence of the $Z$ transform and make sure it includes the unit circle