I know いくつ
means 'how old', but what does いくつか
mean in the following sentence?
緑茶、紅茶、ウーロン茶などいくつかの種類に分けられる。
いくつ in general means "how many"; this can also be applied to years to ask "how old" ("how many years") as you've pointed out.
か can be add to counter question words to mean "several ~".
- ラーメン屋に学生が何人かいます。 → There are several (people) students in the ramen restaurant.
- 先週のお祭りに何個かのたこ焼きを食った。 → I ate several takoyaki (balls) at the festival last week.
- 緑茶、紅茶、ウーロン茶などいくつかの種類に分けられる。 → Tea is divided into several kinds, such as green tea, black tea, and oolong tea.
いくつ can also be used as an interrogative for indefinite number, that is, how many. To use indefinite expressions in non-question, か is combined with it.
I know いくつ means how old
Without context, 「いくつ」 means "how many" far more often than it means "how old".
「いくつか」 means "some", "a few", "several", etc.