[Chem] Balancing and Predicting Chemical Reactions

I'm having a bit of trouble predicting chemical reactions.
I've got decomposition, combination (synthesis), and single displacement reactions down, but I can't seem to figure out how to do double displacements.
I can't figure out why a double displacement reaction would be possible or not.
Here's the problems I can't figure out, can you guys help me out?
I'd appreciate it if you had like a short explanation to why you did what because I need to learn it since I have tests anyways.

Ammonium nitrate plus Barium Hyroxide
NH4NO3 + Ba(OH)2 ---> ?

Ammonium sulfate plus calcium hydroxide
(NH4)2SO4 + Ca(OH)2 ---> ?

Aluminum sulfide plus hydrochloric acid
Al2S3 + HCl ----> ? (I got no reaction, is it correct?)

Chlorine plus Bromine
Cl2 (diatomic) + Br2 (Diatomic) ----> No reaction? Because they're both positive right?

The problem only has the names of the compounds, but I put down what I got so far.

 

These are all reactions that create an intermediate that immediately breaks down into a gas.

In these cases, NH4OH creates NH3 + H2O. The NH3 bubbles out of the solution as soon as it is formed. And in the third one, H2S is a gas that bubbles a well.


Here are the products. You will need to balance the rx's yourself, unless you need help.

-----> H2O(l) + NH3(g) + Ba(NO3)2(aq)

-----> H2O(l) + NH3(g) + CaSO4(aq)

-----> H2S(g) + AlCl3(aq)

-----> No Rx. These do not form any products.

 

How do you know they create an intermediate?
I haven't learned reactions that yield 3 different compounds yet.

 

Well they yield NH4OH, which is very unstable And breaks down into H2O and NH3 gas, so it does form tree compounds in the end.

The last one only forms one product. You may be familiar with these reactions causing insoluble solid precipitates... This is similar, just with a gas.

 

Just as a note: NH4+ will not break down into NH3 in the presence of a strong acid.