1. Sometimes I have to look very closely to identify whether the writer meant to say a typical kind something (or just something) or a lot of something when that person used the word "some"in front of countable nouns. Do you have some guidelines to help me make the distinctions easily? Sorry I can't think of any good examples off my head but maybe this ?

Some example will do.

Some examples will do.

I want some material in that box.

I want some materials in that box.

2. Which one is right?

Whom is this purse belong to?

Who is this purse belong to?
Hi guys,

'Some' can also be used with a singular count noun, to indicate that you don't know about it. It also tends to suggest that you don't much care.

eg Some guy on the bus hurried past me and took the last seat.

eg Some car almost hit Tom.

Best wishes, Clive
Some has a variety of uses. As an indefinite article (like a/an) it modifies plural count nouns and mass nouns.
Some boys walked down the street.
Some cold beer would taste great right now.
I would say some examples and some material. In some cases, the context or knowledge of the world may be needed to decide whether a noun is count or mass.

Number 2 should be To whom does this purse belong or This purse belongs to whom?
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 Clive's reply was promoted to an answer.
Besides being an adjective, some can be a pronoun meaning an indefinite or unspecified number or portion. --- American Heritage Dictonary
Mort didn't see some of the fish.
And finally (?), some may be used adverbially:
Some [approximately] 40 people came to the dinner.
In informal usage, adverbial some may mean somewhat:
The safety of the shuttle has been improved some [formal: somewhat].