All the answers are correct. We land and takeoff into the wind so that our ground speed is the slowest possible ( accelerate/abort energies and landing/braking energies need to be the lowest possible). There are a few exeptions. Some tail wind on takeoff and landing is acceptable IF it has been calculated in the takeoff data.
We also have limitations on crosswind and total steady state wind speed that each aircraft manufacture determines. In the certification of the aircraft the manufacture determines the maximum headwind, crosswind and tailwind the aircraft can handle.
The maximum headwind may simply be based on safety. The MD80 I fly has a maximum headwind of 50Kts. Above this wind I can't land or takeoff. Not because of flight control limitations but because iti starts to become "dangerous". 50kt winds at the surface will probably produce severe turbulance in the lower level of the atmosphere. So its not the speed of the wind. Its the turbulence.
For a crosswind my aircraft has a 30Kt "demonstrated" croswind. They design the aircraft with a rudder for 3 reasons. 1, you need a control on the yaw axis if you want complete control of the aircraft. 2, in a multi engine aircraft, you need the rudder to counteract the yaw tendency if you loose an engine. and 3, during a crosswind landing ( the wind is perpendicular to the runway) you use cross controls to align the aircraft with the runway. So at touchdown the aircraft is not sliding over the ground and touches down in a crab. This puts large loads on the aircraft and is just uncomfortable for the passenger. Now this "demonstrated croswind" is actually demonstrated by the test pilots for the manufacture during the aircraft certification. This is the highest crosswind they were able to show the FAA in a crosswind landing. Above this value you are a test pilot. It can be done but it has not been proven to the FAA and if anything happens, your in trouble.
I had to do this in the C141 aircraft I flew in the military. We had a demonstrated crosswind limit of 32kts. We were landing at Lajes in the Azores. The winds were 50kts perpendicular to the runway. BUT we had nowhere else to go. Santa Maria, the only other airport in the Azores had the same wind and we did not have the fuel to go all the way to Portugal, the nearest land. So we landed, actually wreslted the aircraft to the ground. One of the limitations to the demonstrated crosswind is the rudders abiltiy to rotate the nose to align with the runway. On my aircraft winds above 30 kts. I will have full rudder in and the aircraft will not be completely aligned. We run out of control input.
Now in the New York airport area the flight patterns for all three major airports (LGA, EWR, JFK) is complicated. When the runways are changed at one airport it effects which runways can be used at the other airports due to the arriving and departing flight paths.
One other item. Runways are built based on the wind patterns in the area. If the wind comes out of the north 50% of the time and then the south another 20%. Then a north south runway is what is built so that the aircraft are aligned with the wind. However at times geographical factors may be greater. If you don't have a long section of land available then you do with what you have.
Sorry for the long winded
answer.
Dave