I prefer Magyar Huszar, has a very high utility (bonus dmg vs siege) and just pretty solid stats for a food cost only unit (after the Corvinian Army UT).
That is why its good that the civ can switch techs when needed. If the enemy counters you, you can make the counter-counter. That is why I quite like this civ on my side in a TG. They never become completely useless, no matter what’s the line-up.
It matters less, but not completely irrelevant. It’s a bit of a gamble, whether you want to risk getting hard-countered, or be a less effective generalist, but lower risk of getting hard-countered 
Gold is not completely as fast with trade (trade is less effective than gold miners), so if you use gold units too carelessly, you can still have problems producing enough reinforcements. So mixing in counter units can be beneficial. And if you make too many trade carts, you might also just have too little pop space for army. So again, more tradeoffs in the game you can take (or not take).
Well this is the tricky part, need to also read the civ, and prepare your own units accordingly. I’ve managed to deal with Britons for example, but just needed to make more than one unit type (more than just Serjeants). I 100% agree with you that a pure 100% Serjeant army is not always going to be very good at all, depending on what the opponent is.