Yes, it is correct to hyphenate "modern-day" when it is used as an adjective to describe something that pertains to the present or current time period. For example, "modern-day technology" or "modern-day issues."
You would hyphenate "thank you" when it is used as an adjective before a noun, such as in "a thank-you card."
You can hyphenate the word improvement like this: im-prove-ment.
The number is forty one (41). When you use it as an adjective, hyphenate it as in "forty-one dollars."
Yes, "hundred million dollar project" is often hyphenated when used as a compound adjective before a noun.
For names ending in "s," you can follow the standard rule for hyphenation by adding an apostrophe and an extra "s" after the name. For example, "Thomas" would be hyphenated as "Thomas's."
Always!
The correct spelling is 'hyphen'.
Modernday Folklore was created on 1995-06-27.
You don't. The way you have it written in the question is correct.
It's correct but I would hyphenate the two words.
That is correct, but you would hyphenate it as heart-wrenching (causing sorrow or despair).
No, in general it is not correct to hyphenate certain prefixes, co-, pre-, mid-, de-, non-, anti-, etc. You therefore write preordain instead of pre-ordain, antidote instead of anti-dote, and midnight instead of mid-night.
You do not need to hyphenate.
You do not hyphenate the number.
You would hyphenate "thank you" when it is used as an adjective before a noun, such as in "a thank-you card."
Don't hyphenate; ongoing is one word.
You hyphenate it only at the hyphen.