Learn Finnish: Löysitkö vanhan omakotitalosi netistä? - Did you find your old detached house on the internet?

This is because of the verb löytää (to find). In Finnish, you don't find something in a place; you find it out of or off of a place. Verbs of searching and finding require the elative (-sta/-stä) or ablative (-lta/-ltä) cases. So you found the house out of the internet (netistä).

Why is the adjective vanhan in the genitive/accusative case (ending in -n), but the noun it describes, omakotitalosi, doesn't end in -n?

The noun is actually in the genitive/accusative case too! However, when you add a possessive suffix like -si (your) to a noun ending in the genitive -n, the -n is dropped. So omakotitalon + -si becomes omakotitalosi. The adjective vanhan keeps its -n because adjectives don't take possessive suffixes.

Why is the past tense stem for löytää (to find) löysi- instead of löyti-?

Many Finnish verbs that have a t before the final vowel change that t to an s when forming the past tense. When you add the past tense marker i, the t shifts to an s before it, making the past tense stem löysi- before adding the personal ending -t.