One thing that affects x-wind landings significantly (regardless of size) are swept wings.
If you consider that lift is basically generated perpendicular to the leading edge you will see why.
On a light ac the wings are straight and in a headwind the windspeed all provides lift and equally on either wing.
Imagine a wing with a sweep of 45 degrees! Draw a very simple sketch if it helps. In a headwind only part of that windspeed produces lift (windspeed cos 45degrees = 0.7xwindpeed - who said that you would never use o-level geometery?) but still equal on either wing.
Now picture the wind from 45 degrees off the nose.
In your light ac both wings still have the same lift component from the wind (wind x cos 45).
However in the swept wing: The upwind wing is now effectively 'straight' (100% lift from wind) but the downwind wing is parallel to the wind (zero lift from wind!)
You can see that gusty x-winds in a swept wing can be a tad tricky!
This is more noticeable in lighter jets due to lower inertia in roll (and also not emost commercial ac have wing sweep of less than 45 degrees!)
On your light ac you may have been taught the 'wing-low' method where you try and turn (bank) into the wind and keep straight with rudder. This allows you to set up and stabilise your approch early and not panic when the gound rushes up. The downside of this approach (touching upwind wheel first) becomes critical when you have under wing engines with very little clearance!
'Big boys' use the other method where you point the nose into wind and 'crab' towards the runway. At the last minute strighten the ac with rudder (so the wheels point down the runway) But the secondary effect of rudder and yaw is roll (by yawing you are making the 'outside' wing fly faster and create more lift) so you musrt smoothly counteract that with aileron input during the flare.
Either method works in light ac but the latter requires anticipation at a critical moment so is sometimes considered less appropriate for the inexperienced who may resemble a bunny in the headlights when everything happens quickly!
Apologies to those who found the above patronising and to those who got lost - not sure of the correct level in this forum!
Edited to add:
Sorry, actually ingnored your questions!
1) An ac with autoland will also land in a x-wind (remember it might only be 1 knot!) but there will be a limit. Doesn't apply to me so afraid I don't know
2) It can be a battle - but only because your average cessna wont be flying in 30 knot gusts coming directly from the side! It is only more sporty because we can't choose to sit in the club bar drinking coffee! (although if it is unsafe we obviously would) So for a given wind strength we probably find it easier. (unless the cessna has an into wind runway
