Are there specific rules on subject-verb agreement?
If so, what is the general rule in it?
What are the rules when there are compound subjects connected by an "and" or an "or"?
They're just really quick questions; I'd appreciate any quick help to it. 
The basic grammar rule in English is, of course, the subject-verb agreement rule. It prescribes that the operative verb of a sentence should always agree with its subject in number. This means that a subject that’s singular in number should take a verb in the singular form, and that a subject that’s plural in number should take a verb in the plural form.
Here, just by way of review, are examples of the basic application of this rule:
Singular subject (“singer”), verb in singular form (“sings”): “The
singer sings so beautifully.”
Plural subject (“singers”), verb in plural form (“sing”): “The
singers sing so beautifully.”
A notable exception to this rule, however, is the pronoun “you.” It takes a plural verb whether it is in its singular form or in its plural form: “
You [singular sense, meaning just one singer]
sing so beautifully.” “
You [plural sense, meaning two or more singers]
sing so beautifully.”
As a general rule, a compound subject of a sentence—meaning that the subject consists of two nouns linked by the conjunction “and”—requires a plural subject, as in “When properly motivated,
the singer and the orchestra perform beautifully.” There are exceptions to this rule, though. The notional sense of unity between two subjects can sometimes prevail over grammatical agreement, such that the compound subject—although plural in form—takes a singular verb: “
Her name and e-mail address is [not
are] listed in my directory.” “
My better half and only love has been [not
have been] faithful to me all these years.” “
The long and the short of it is [not
are] that we parted ways.”
We must be aware, too, that the subject-verb agreement rule fails when sentences have two subjects, one singular and the other plural, such that the verb can’t agree in number with both of them. Consider this sentence: “Either Teresa or her sisters i
s/are not being truthful about what happened.” Which of the subjects should determine the number of the verb—the singular “Teresa” or the plural “sisters”?
To resolve the dilemma, English uses the so-called “agreement by proximity” rule. This rule says that in the case of compound subjects in “either…or” constructions, the verb should agree in number with the subject closer to it. Thus, by virtue of the proximity of their subjects to the verb, these sentences are both grammatically correct: “
Either Teresa or her sisters are not being truthful about what happened.” “
Either her sisters or Teresa (herself) is not being truthful about what happened.”
And here’s another complication to the subject-verb agreement rule that we must beware of. When a singular subject is followed by the conjoining prepositional phrases “as well as,” “in addition to,” and “along with,” the accepted usage is that the verb in such constructions should be singular: “
Gerry as well as Tony works [not
work] in my office.” “
The necklace in addition to her bracelet is [not
are] missing.” “
The summer cottage along with the adjoining farm is [not
are] for sale.”