Can two people use one Pay-Per-Ride MetroCard in New York for one ride?

Yes, up to 4 people can use one Pay-Per-Ride MetroCard.

So my question is, if I use "Pay-Per-Ride MetroCard", does it only cost $2.75/ride for both of us? Because it states that "up to 4 people can use one Pay-Per-Ride MetroCard".

One card can be used for 4 persons but it needs to be swiped 4 times and the cost will rise with each swipe. One swipe($2.75) for 4 persons is a No No.

Or do we need to swipe it twice which will us cost $5.50/ride?

Yes. You are 2 people so the cost will be according to that. Here's how you can use Pay-Per-Ride for the both of you.

With Pay-Per-Ride MetroCard you can pay for up to four people at one time and all four can transfer together free. When you swipe or dip your MetroCard on the first mode of transportation you will need to swipe for each person traveling. At your transfer point you will only need to swipe (at a subway turnstile) or dip (on a bus farebox) ONE TIME for you and your travel companions to enter into the subway system or board a bus. Note that the number of travel companions must remain the same for the transfer.

Source: MTA

Do Not buy 1 Unlimited ride card for 2 people, it will not work. It is for 1 person and can not be used more than once per 18 minutes at the same station. If you are considering buying Unlimited Ride card buy 1 for each person.

This 18 minutes period on the same station is to forbid the use of this card by multiple people for the same trip, otherwise it does not matter if you take a return trip or transfer to some other line within those 18 minutes.

An Unlimited Ride MetroCard cannot be used again at the same subway station or the same bus route for at least 18 minutes. Cannot be used by or transferred to another person until the completion of a trip for which entry was obtained.

Source: MTA

So if you are travelling somewhere alone you can use your Unlimited ride, then for some other journey if your friend is travelling alone he/she can also use your card but if you're travelling together on a journey it will not work.