Indeed.
Nothing, because you don't have a complete circuit - but there will be no voltage between the free ends.
Again nothing, but you will have twice the voltage between the free ends.
WRONG - you get a short circuit.
Parallel, out of phase would mean each battery's positive terminal connects to the other's negative - if that won't cause a huge current circulating through the batteries, I don't know what will. If you connect a load in parallel with these paralleled batteries, you will get very little current in the load, as it is all going between the batteries.
In my world, "parallel, in phase" means that the positives of the two batteries are connected together, and to one end of the load, if any, and the two negatives are likewise connected together, and to the other terminal of the load. The voltage across the two parallel batteries will be equal to the voltage of one battery, and no current will flow, unless a load is connected.
I went to school, and have been working in electronics for 45 years - I think I know what I'm talking about here. (and I have two 12 volt batteries paralleled "in phase" on my boat, with no problems.)