for first para, you're pretty much right.
all vehicles' manuals will specify what wattage their headlights
are using. you'd know what type of bulbs you need to buy (eg H4, H3
etc) as well.
if you use a bulb with higher wattage, the bulb socket can melt
away with time.
not sure if a relay will solve the problem. but i think it's safer
to stay within the specified wattage. the socket stays in a piece,
and the bulb functions proper.
hope it helps.