No, pants, trousers, britches, pantaloons are plural nouns that refer to a single garment. I can only find "pant" as a singular noun in in connection with another noun as in "pant leg" or "pant skirt." "The pant" as a garment doesn't exist. You can translate "Hose" (singular) as "pants" or "a pair of pants" .
So if you say in German, "Ich habe heute 3 Hosen gekauft" The best translation would be "Today I bought 3 pairs of pants."
This should help http://german.about.com/od/grammar/a/The-Position-Of-Nicht.htm
The following link provides a more comprehensive approach to working out where the nicht goes if you have the time to read it, but you might need to come back to it when you understand the structure of German subordinate clauses (if you don't already that is) https://yourdailygerman.com/2016/06/23/position-nicht-german/
It's just a fact.
Some nouns form their plurals with an umlaut, some don't.
I'm sure there are historical reasons but unless you learn Old High German, there's probably no rule one can see inside the modern-day language.
Sometimes, the same word-form even forms a plural both with and without an umlaut, when there are two words that look the same in the singular but not in the plural, e.g. Wort has plurals Worte and Wörter, and Ausdruck has plurals Ausdrucke and Ausdrücke.
That would surprise me - though mistakes do happen, I think you may be misreading the entry: perhaps applying the "pl" that belongs to the English words "trousers" or "pants" to the German Hose instead of the "f" that it should have.
Anyway, even if your dictionary does have an error, die Hose is feminine singular in German.
(The plural -- for multiple pairs of trousers/pants -- is die Hosen.)