‘As is the father so is the son.’
Is this a proverb?
What does it mean?
Is this sentence grammatically correct?
Yes, it would be called a proverb. It just means that sons tend to resemble their fathers. Yes, it is grammatically correct, but “as is … so is …” is an old-fashioned or literary pattern.
Perhaps a better-known variant of the same proverb is: “Like father, like son.” (Also: “Like mother, like daughter.”)
A similar saying is “The apple does not fall far from the tree.”
And here is an interesting saying with an entirely different meaning - can you figure out what it means? “The child is the father of the man.”
Off the top of my head, I read this as: what you become as a man depends on what habits, traits of character etc you pick up while you are a child.
Exactly correct - I need to come up with some more difficult questions!
I would’ve never figured that one out – at least, not without any context.
Of course, I knew this one! In my language we say: “The splinter does not land far from the trunk.” 
By the way, are these OK to say here:
Sorry, I’m straying away from the topic.
Sorry, I’m straying off topic.
Thank you.
Perfectly okay.
Thank you, Bev.
Beeesneees,
Can I say as below:
“Sorry, I’m straying off the topic.”
Is the use of ‘the’ not required?
You don’t need ‘the’.
While Luschen is looking for some cracker of a saying, would you take it as a warming-up:“A closed mouth gathers no feet”.