To answer the first part of the question one procedure is very simple.

FIR filter can be obtained or constructed as a difference of two IIR filters.

Simple representation:

(IIR filter) - (Delayed and scaled IIR filter) = (Truncated IIR) FIR filter

Excuse me, but I did not understand what you mean.

Saurabh Kumar is correct.

for an IIR to FIR, presume that transfer function can be represented like T(z) = N(z)/D(z), thus 1/D(z) can be expanded and truncated to required order of FIR filter.

Also for FIR to IIR conversion delay the output and feed it back after some delay.