How does a catalyst work in speeding up a reaction?

Which of the following reactions is reversible?

What is the equilibrium constant expression for the reaction:

2 BrF_5(g) —> Br_2(g) + 5 F_2(g)

Calculate the equilibrium constant for the following reaction:
SO₂ (g) + NO₂ (g) <=> SO₃ (g) + NO (g)
[SO₃] = 0.40 M, [NO] = 0.30 M, [NO₂] = 0.15 M, and [SO₂] = 0.20 M.

Which is the correct equilibrium constant expression for the following reaction?

Fe₂O_3(s) + 3 H_2(g) —> 2 Fe_(s) + 3 H₂O_(g)

If the concentration of SO_{2 (g)}  is increased, the equilibrium of the reaction will _____.
SO_{2 (g)} + O_{2 (g)} <−>  SO_{3 (g)}

If the heat is removed from the chemical system, the equilibrium will _______.
heat  +  N_2(g)  +  O_2(g)  <−>  2NO_(g)

If the pressure in the following system is increased, the reaction will ____________.
N_{2 (g)} +  3 H_2 (g) <−> 2 NH_{3 (g)}