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Как же здесь оказались книги, которым больше семи веков?
I'm a bit stumped with this part...
1) Why use the dative relative pronoun "которым" rather than the nominative?
2) I suppose "больше семи веков" means "more than seven centuries". Is "семи веков" in the genitive because "больше", just like "много", takes the genitive case?
This is so called "dative of possession".
It's used for things like age, name, kinship etc. instead of possessive or genitive:
(возраст) мне семь лет
имя мне легион
я ему отец
человек человеку волк
and so on.
Note that this is a thing in Latin as well: nomen mihi legio est, homo homini lupus est, etc.
All comparatives without чем govern genitive. Пёс больше кота, толще кота, красивее кота. Автомобиль дороже велосипеда, тяжелее велосипеда, быстрее велосипеда.
There is an expression about age with dative: кому-то (или чему-то) столько-то лет (дней, месяцев, веков etc.) Этим книгам больше семи веков is an example of such expression. Since которым replaces этим книгам, it should be in dative.
1) This is a normal way to talk about ages in Russian:
Ему(dat.) десять лет. - He is ten years old.
There is (was) a kind of verb implied in this sentence which is used with dative noun:
Ему [уже] исполнилось десять лет.
2) Yes, больше takes genitive (if it is in the same clause). You may say either
Десять больше пяти(gen.).
or
Десять больше, чем пять(nom.).
