Learn Finnish: Huomaan varjon, ja talossa on jokin. - I notice a shadow, and there is something in the house.

In standard Finnish, jokin is used for things or animals ("something"), while joku is used for people ("someone"). Since the speaker is talking about an unknown thing in the house, jokin is the right choice.

Why does varjo (shadow) end with an -n here (varjon)?

It is the object of the sentence. Because you notice the whole shadow (a complete action), the object takes the -n ending (the accusative case). If it were an ongoing action or a negative sentence, it would take the partitive case (varjoa).

Why is the word order talossa on jokin instead of jokin on talossa?

This is an existential sentence, which states that something exists in a particular place. In Finnish, these sentences usually start with the location (talossa), followed by the verb (on), and end with the new thing being introduced (jokin).

What is the base form of the verb huomaan?

The base form is huomata (to notice). It is a Type 4 verb. To conjugate it for "I", you drop the -ta, lengthen the final vowel to get the stem huomaa-, and add the personal ending -n.