We had a lot of difficulty in finding the place

We had lot of difficulty in finding the place

We had lot of difficulties in finding the place.


And also when is people taken as singular and plural?

There is much people

or


There are many people

or if both are correct.

We had a lot of difficulty in finding the place.

We use either 'a lot of':
"He ate a lot of the pie."
"A lot of people said they were coming but didn't show up."

or 'lots'
"These days, lots of cars are painted with metallic paint."
"Lots more cars can be transported in container ships than in ordinary cargo ships."
"The children had lots of fun at the beach."

'person' is singular, and 'people' is plural.
"The person who stole my wallet was caught."
"There are many people who…"

'much' is used for non-count nouns, and 'many' is used for 'count' nouns.

(1) We had a lot of difficulty in finding the place.
(2) *We had lot of difficulty in finding the place.
(3) We had a lot of difficulties in finding the place.
(4) We had lots of difficulties in finding the place.
(5) *We had lot of difficulties in finding the place.

Singular "lot" requires "a" as determiner, as in (1) and (3), so (2) and (5) are ungrammatical. Plural "lots" requires no determiner as in (4).

(6) There are many people here.
(7) There are fifty people here.
(8) There is one people person here.
(9) There is much are many people here.


"People" has only a plural interpretation here, so (6) and (7) are okay, but in (8) singular "one people" is ungrammatical; instead we have "one person". Count nouns like "people" take "many" as determiner, but not "much" which is used only with non-count nouns.

(* = ungrammatical)

PaulM