To that spending a lot of time learning spelling: Not really. IIRC I was in 5th or 6th grade (=11 or 12 years old) when we learned most of the cases, 11 of the 14, 15, 16, or 17 (Arguably some cases aren't actually cases...) to say exactly. Knowing what the cases are called doesn't really make any difference to wheather you can read or write though. They're used in normal speech all the time (so no extra need in learning them).
When you think about it, if you have learned the alphabet, you can write and read already. Each letter corresponds to it's specific speech sound. All speech sounds are equal in lenght. All letters (=speech sounds if you like) are always pronounced the same way. The stress in words is always on the first syllable.
Things I can come up with that you have to learn seperately are perhaps Grammatical moods (=imperative, indikative, konditional, potential, the rare eventive and optative, AND the recently found aggressive. (The aggressive form being half a joke in the first place eg. Vittumä / Vittu mä sulle näytän... = **** (you), I'll show you.... The structure consists of ****+pronoun. You can form this structure also without the f-word btw)) since they aren't used that often.
The other major thing must be compound nouns which work like in German. You can add words after each other forming new words eg. Pien/talo/sähkö/kilo/watti/tunti/mittari is a gauge to measure the electricity consumption of a detached house in kilowatt hours.
Ain't grammer fun!