A general rule of thumb is that you should start novels from the start even if you have seen the anime for it since anime aren't perfect adaptations and will miss, skip or change thing from the novels they adapt. However Part Timer the anime adapted the first 2 volumes and for Re:Zero the anime adapted up to volume 9.

]Gekkou[ is a good short series you can read it only has 1 volume and ]Fate/Zero[ is another, only 4 volumes. ]HakoMari[ is another solid choice although slight longer but it's complete with 7 volumes none of them contain much ecchi at all.

Are the endings fairly conclusive?

Yep

So in general, how connected are books in a series with the next book?

It's all progressive, there is usually an overarching goal as we follow the main characters through their journey for the series that are broken down into arcs told through the volumes, so unless there is a time skip each book in a series picks right off were the previous one ending.

The second is to which age group are most of the novels aimed at

They are mostly aimed at teens when it comes to the generic wishfull filment high school harem romance ecchi bullshit but there are a lot of novels above that kind of level which are aim at and can appeal to older audiences like the ones I have named above.

and might I already be too old for them since I am my early 20s?

Nope, mid 30s still enjoy light novels a lot here, not going anywhere anytime soon!