Re: latter, later
If I were speaking about the context you gave, I would also say "the second half" or the "last part" etc. However, in a film review, where someone has actually watched the whole film, they might say "In the latter part of the film, the characters really start to come alive". It's a way of differentiating it from the earlier part of the film. It's not possible to turn up late to a film and then somehow see the first half but not the second half.
The more usual use of "latter" is as the opposite of "former", when two items are mentioned. "I have both milk and cheese in the fridge but I think the latter has now gone out of date".
We do say "In the latter part of the evening" which, to me, would probably mean from about 10pm to midnight. Note, though, that we don't say "the former part of the evening". We would say "the early part of the evening".
Remember - correct capitalisation, punctuation and spacing make posts much easier to read.