Digital Signal Processing Filters Problem
I have worked out H(z) to be (0.4 + 0.6z^-1) / (1-0.8z^-2) is this correct?

Close but one detail is wrong

Is this filter an FIR or IIR type?

Look at the pole locations

How do you determine the poles and zero?

Poles are the roots of denominator polynomial. Zeros are the roots of the numerator polynomial.

How do you determine if the filter is stable or unstable?

Look at the pole locations
These questions are about as fundamental as it gets in DSP. They are also incredibly simple, in fact, so simple that it's hard to give a hint. If it takes you more than a few seconds to answer this, you need to adjust the way your are studying. I strongly recommend to not proceed to any more advanced topic until you very comfortable solving this type of problems. It's fundamental to whatever comes next.