magnus opus wrote:Less- is to be used for unquantifiable quantities.
Fewer- is used for countable entities.
Lower- is also used for countable quantities.

the last one of these isn't really correct -- "lower" is generally used for numerical abstractions, such as level, quantity, rate, figure, percentage, etc.
... or for things that aren't really numerical but still have higher and lower levels, e.g., significance, importance, etc.
note that all of these quantities are actually UNcountable. for instance, you would say "less significance", not "fewer significance".

i think that's the source of the confusion here. if you say something like a lower number of dogs, that the word "lower" applies to number, not dogs.

1.When do we use Lower and when do we use Fewer?

see above.

2. We say population is unquantifiable like workforce, so it should use less instead of fewer, but don't we say U.S has a population of 500 million.(which is quantifying it? Please explain this paradox.

yeah, but this is the case with ALL numerical quantifiers.
level
quantity
number
figure
rate
percentage
proportion

you wouldn't use "fewer" with any of these. the numerical quantifiers themselves are uncountable, although the things that are being counted are, of course, countable.

e.g.
there are fewer dogs in my house than in your house.
the number of dogs in my house is lower / less than the number of dogs in your house.

3. Are numbers not quantifiable? we say 3 is less than 5 ( not fewer) why is this so?

same deal as above.

note that sentence correction problems are not going to be talking about pure numbers -- a sentence correction problem is clearly not going to have something like "five plus five" -- so this concern is irrelevant, but it still fits the pattern above. (i.e., you are not going to see a sentence correction problem involving numbers, unless they are either (1) numbers OF something or (2) labeled numbers such as percentages.)