1. Will a precipitate form if solutions of potassium sulfate and barium nitrate are combined? If so, write the net ionic equation for the reaction.

Question

2. Will a precipitate form if solutions of potassium nitrate and magnesium sulfate are combined? If so, write the net ionic equation for the reaction.
3. Will a precipitate form if solutions of barium chloride and sodium sulfate are combined? If so, identify the spectator ions and write the net ionic equation.
4. Write the net ionic equation for the precipitation of nickel(II)sulfide.

My answer:

1. no rxn
2. no rxn
3. no rxn
4. Ni2+ (aq) + S2- (aq) ---->NiS (s)

Answer 1

I don't believe you know the solubility rules. Here is a simplified set.
http://www.files.chem.vt.edu/RVGS/ACT/notes/solubility_rules.html

So the answer to 1 is yes because BaSO4 is insoluble.
The answer to 2 is no because KNO3, MgSO4, K2SO4 and Mg(NO3)2 are soluble.

If the answer to 1 is yes then the answer to 3 must be yes, also.
Your answer for 4 is right.
You need to write the net ionic equations for the others and identify the spectator ions.

Answer 2

you got this wrong because all of them are except for number 2