What's the only room from which no one can enter or leave

Dwayne Johnson was running away with the loot from a heist in his car along with Vin Diesel. One tire was punctured and he dropped down to replace it. While changing the wheel, he dropped the four nuts that were holding the wheel and they fell into a drain. Vin Diesel gave him an idea using which they were able to drive till the rendezvous point.

What was the idea ?

10 people came into a hotel with 9 rooms and each guest wanted his own room. The bellboy solved this problem.
He asked the tenth guest to wait for a little with the first guest in room number 1. So in the first room, there were two people. The bellboy took the third guest to room number 2, the fourth to number 3, ..., and the ninth guest to room number 8. Then he returned to room number 1 and took the tenth guest to room number 9, still vacant.
How can everybody have his own room?

Can you find out the remainder when 3^300 is divided by 5?

Living above a star, I do not burn
Eleven friends and they do not turn
I can just be visited in a sequence, not once or repeatedly
PQRS are my initials
Can you tell my name accurately?

I am the black child of a white father, a wingless bird, flying even to the clouds of heaven. I give birth to tears of mourning in pupils that meet me, even though there is no cause for grief, and at once on my birth, I am dissolved into air. What am I?

Can you replace the question mark with the correct letter?

6 + 6 + 6 = N
7 + 7 + 7 = E
8 + 8 + 8 = R
0 + 0 + 0 = ?

What is the word or phrase?

In order to complete the racing competition, the Mexico racetrack has to submit its top and the most famous three horses to win the competition. Due to an electrical storm, all the records are cleared and no one knows which horse holds the record. They all look identical and it becomes even more difficult to differentiate the horses. There are 25 horses in the Mexico racetrack. But there can be only five horses at a time on the track. What will the least number of races that can be conducted to find out the three fastest horses?

Pronounced as one letter,
And written with three,
Two letters there are,
And two only in me.
I am double, I am single,
I am black blue and grey,
I am read from both ends,
And the same either way.