"Should of" is a misspelling of "should've"; "should've" is pronounced the same as (or very close to) "should of". It is indeed incorrect to use "should've" for future event. It should be just "Next time, she should flush the toilet."
This is not specific to God; it’s simply about the uncommon tense of the verb.
“[May] God bless” and “[May] God damn” are in the subjunctive (you’re hoping He blesses or damns the object), which does not add the “s” in the third person singular as in the simple present.
The sentence is perfectly idiomatic (at least in American English): it is a conditional in proper form.
A purist might say, given that the speaker intends to show a picture almost immediately,
This will make more sense once you see a photo
is a better form of conditional, but that is an opinion about style.
"Programs for exploring space" is fine. The other option would be "programs to explore space". The difference is whether you want to state reason or purpose.
I bought a pan for cooking eggs (cooking eggs is the purpose of the pan)
I bought a pan to cook eggs (cooking eggs is the reason you bought the pan)
"God Bless" is a request, one is asking God to bless something or someone. Similarly, "God damn" is normally asking God to damn someone or something, at least in metaphor. "God damn" is not as often used in its original literal meaning these days. These are in the imperative and that is the form used.
One could say:
"Any" is just a modifier for this purpose - the number of the noun it modifies is unchanged:
If I see any merchandise out of place, I'll fix it. (mass noun)
If I see any item out of place, I'll fix it. (singular noun)
If I see any items out of place, I'll fix them. (plural noun)