No 1
Book your ticket to the top of the Eiffel Tower in advance, and skip the queues! Otherwise you should expect to queue for 2 hours, if not more.
There is no limit to how long you can stay at the top. You should aim to be there well before sunset as there is still some queuing and security, plus it takes a while in the 2 lifts required to reach the summit.
It is open every day of the year - Last entry is 9am to midnight from 21 June - 2 September, and from 9:30am to 11pm the rest of the year.
Alternatively you can take the 341 stairs to the midway level, before taking the lift to the top. This is a cheaper option and if without a reservation can save some time in the queues. Note the stairs shut at 6pm from September to June.
Or for a real treat you can book a table at the midway restaurant '58'
Eiffel tower website