The sentence Authentic Italian cooking is very healthy —— witness the low incidence of heart disease in Italy. is an example of parataxis: two short complete sentences that are combined without any conjunction. Without changing anything, you could actually rewrite this sentence like so:
[Authentic Italian cooking is very healthy.] [Witness the low incidence of heart disease in Italy.]
The first sentence Authentic Italian cooking is very healthy is a normal declarative sentence, but more importantly, the second sentence Witness the low incidence of heart disease in Italy is indeed an imperative sentence (as @Jack-oflaherty's answer says). As such, it doesn't have a subject, and like in all English imperatives, the verb occurs in its base form without any inflectional suffix.
This answers your questions:
- What is the subject of witness in the sentence?
Authentic Italian cooking is the subject of the first sentence Authentic Italian cooking is very healthy. The sentence Witness the low incidence of heart disease in Italy doesn't have a subject, as English imperative sentences are subjectless.
- Why isn't witness in the third-person singular form?
In English, imperative sentences are not marked for number, person, or tense, but feature the verb in its bare form (here: witness, not witnesses).
- Can we take it as an imperative sentence?
Yes, absolutely – but only the second part witness the low incidence of heart disease in Italy, not the first part Authentic Italian cooking is very healthy. This is a declarative sentence.
By the way, your rephrasing changes the grammatical structure from parataxis to hypotaxis, or more conventionally, to a complex sentence with a subordinate clause:
[Authentic Italian cooking is very healthy [as witnessed by the low incidence of heart disease in Italy] ].
This type of subordinate clause (sometimes called passive-participle clauses) is also subjectless, and it uses the past participle form of the verb (as seen, for instance, in the sentence Authentic Italian cooking is very healthy as eaten by the natives in Italy, where the past tense form ate would not be possible).