No. It should be New Year Party.
Yes, when it is New Year's Eve or New Year's Day. They are possessives, as in the day that belongs to a new year. If you are talking about plurals, then there is no apostrophe, like "New years are not like old years".
Yes, in the phrase "last year's party," you should use an apostrophe to show possession. The apostrophe indicates that the party belongs to last year.
yes
It depends. If you are talking about "the year's best game," there's an apostrophe. If you're talking about "two or more years," there is no apostrophe.
The possessive apostrophe. Does the party belong to Emmerson? or is the Party made up of multiple Emmersons? If the former you need it, the other you do not - but the construction would be odd - a Party of Emmersons being better in the second case.
yes
I believe it should have an apostrophe, but it is often left out. It's the first day of, or belonging to, the New Year. It is the New Year's first day. Within a generation or two, we will probably never see the apostrophe used for New Year's Day; it will go the way of archaic usage. If current trends are any indication, apostrophe ess will probably shift from indicating the possessive forms of most nouns (its current use) to the general plural form (still considered incorrect currently).
Alice's New Years Party - 1910 was released on: USA: December 1910
YES
No, the sentence "She has almost 30 years experience" does not require an apostrophe after the s in the word years. The word "years" is used as a plural noun in this context, describing the duration of experience, so no apostrophe is needed.
No, "years time" is typically written without an apostrophe.
A party involves more than one person so it wouldn't really be a party.