Manual transmissions in light-duty vehicles have lower towing ratings than automatics, because drivers tend to burn out clutches with heavy loads on light vehicles.
European towing ratings are routinely much higher than North American ratings, and it has nothing to do with structure, axles, suspension, brakes, or the hitches (the Euro standard for recreational trailers is a 50 mm ball, that's slightly under 2" diameter). The difference is due to different conditions, including lower speed - in most European countries cars towing trailers are limited to 80 km/h (50 MPH) and wouldn't normally go very far per day, while here people expect to tow at 100 km/h or more all day. Euro trailers are also different, with the mass more concentrated in the middle for better stability so they can get away with less tongue weight, so handling the weight on the hitch is less of a concern.
There's no reason a manual transmission can't be designed with a better towing capacity rating, all manual (proper) Landrovers can tow upto 3500kg - 7700Ibs (which is the maximum allowed for the 50mm euro ball hitch) Can go higher upto 'I think' 4000kg (8800Ib) with coupled brakes and a different hitch but then you start getting into 'commercial' type driving licences.
What would normally result from the lower towing weight limit implied to manuals is if they have reused a transmission/clutch from a lower powered/smaller vehicle - the Landrover Freelander series I for example re-used a car manual transmission and the clutch was no good for HD off roading or towing.
When vehicles are certified for towing in the UK, the trailers used are not caravans - they are usually smaller/lower and more dense - so less effected by cross winds, so while 'legally' you could tow a 3.5 tonne caravan (not even sure if there is a 3.5T caravan for sale in the UK - most max out arround 2T) its probably not recommended - due to cross wind stability. the caravan club have a ruel of thumb for caravan weights (not a legal limit) of upto 80% of the tow vehicle's GVM or upto 100% for experienced drivers - with obviously ideal weight distribution.
In addition to the certified max towing limit, vehicles are also rated for their maximum down load 'D'/tongue weight the hitch can take - along with their max train weight - Legally none of these can be exceeded.
Regarding speed limits - UK (my home country) speed limit when towing a caravan on a motorway is 60mph, with many big SUV's (Rangerovers etc) 'illegally' doing more like 65 - 70+mph.
In Europe the speed limit is varied and includes weather condition (bad weather - lower speed) but seems to be between 50 - 60mph with gross train weight above 3500kg (7700Ibs) and 50 - 80mph with a gross train weight less than 3500kg (7700Ibs)
A game changer on modern vehicles in Europe (do you have it in the US?) is TSP (trailer stability program) where vehicle sensors monitor for snaking/yaw while towing and use the ABS/Traction systems to counter act it & correct it.
Also we have friction hitches (do you have these in the US?) where the caravan hitch has friction pads which clamp a dry tow ball, again to reduce snaking.