Learn Swedish: Grannen är oförskämd och ovänlig. - The neighbor is rude and unfriendly.

It works exactly like the English prefixes un- or dis-. Since vänlig means friendly, adding the o- prefix creates its direct opposite: ovänlig (unfriendly). It is the most common way to form negative adjectives in Swedish.

If oförskämd means rude, can I just remove the o- and say förskämd to mean polite?

No, you cannot. While ovänlig has a direct, usable opposite in vänlig, the word oförskämd is a set expression for rude or impudent. The word förskämd does exist, but it means spoiled (like rotten food), not polite! To say polite, you would use a completely different word like artig.

Why don't oförskämd and ovänlig end in -a here, since grannen (the neighbor) is in the definite form?

Because they come after the verb är. When adjectives describe a noun from across the verb, they only match gender and number (en, ett, or plural). They do not take the definite -a ending. You only use the -a if the adjective comes directly before the noun, as in den ovänliga grannen (the unfriendly neighbor).

Where does the stress go when pronouncing words with this negative prefix, like ovänlig and oförskämd?

The pitch and stress almost always fall heavily on the o- prefix itself. You emphasize it as O-vänlig and O-förskämd. Putting the weight on the prefix helps make the negative meaning instantly clear to the listener.