Learn Finnish: Katsoin tv:tä koko illan. - I watched TV the whole evening.

You pronounce it as "tee-vee-tä". In Finnish, when you attach a grammatical case ending to an acronym or an abbreviation, you must separate the base word and the ending with a colon.

Why is the time expression illan in the genitive/accusative case instead of the partitive?

Time expressions that show the total duration of an action (meaning you did it for that entire specific block of time) act like total objects. They take the accusative case, which looks exactly like the genitive -n here. If this were a negative sentence (I didn't watch), it would take the partitive iltaa.

If illan takes an -n ending, why doesn't the adjective koko change to match it?

Koko (whole/entire) is an exception to the standard rule where adjectives must agree with their nouns. It is an indeclinable word, meaning it always stays exactly the same, no matter what case the noun following it is in.