The general rule is that if you use a singular noun you must use a singular verb and if you use a plural noun, you must you a plural verb.
No. This is wrong.
The verb agrees with the subject.
The verb is "would"
So we look at the verb table for would
(Past tense verbs are easy!)
The subject ...
As with your other question, you seem to be very confused about noun-verb agreement.
The noun which the verb must agree with is the subject, which in your sentence is "you." As it is an interrogative sentence the verb comes first, so "did" is the main verb which must agree with the subject "you."
The bare infinitive "do&...
Those is plural, but Which of those is a selection from those, and could be singular or plural - more often singular, I think.
Like is neither singular nor plural: as it is governed by a modal (would) it is the base form of the verb.
You is a pronoun which can be singular or plural. Here it is probably singular, but not necessarily - depends on how many ...
A 'cast' on a limb or part of the body, sometimes 'plaster cast', is a cover, often made of plaster, which is used to protect a broken bone by keeping part of the body stiff.
Plaster cast (Collins Dictionary)
I think neither construction is quite right (though both would be understood). Using "software" is ungainly.
I would write
Images were processed using GIMP (or ImageMagick, or Photoshop, or Mathematica).
If you want to call attention to a particular algorithm, rewrite accordingly:
Images were sharpened using GIMP (or ImageMagick, or Photoshop, ...
It was not a wolf,” Brienne heard herself say.
"Say" is a verb.
"It was not a wolf" is the main clause, and "Brienne heard herself say" is a parenthetical, a form of supplement.
Note that syntactically the noun phrase "herself" is the direct object of "heard", and semantically the understood subject of the ...
"but usually when we use 'by' we don't put a/the/my before noun. Can somebody explain me why we did that here?"
The statement above is not accurate:
I was bitten by a dog, not a cat. [general statement]
I was bitten by the dog in the street, not the one in the house. [specific statement]
I was bitten by his dog last night. [specific statement]