Learn Finnish: Lihava pelle on notkea. - The fat clown is supple.

You would ask Millainen pelle on notkea? or Minkälainen pelle on notkea? Since lihava (fat) is an adjective of quality, millainen or minkälainen is the exact question word you need to prompt it as an answer.

If I wanted to ask "What is the fat clown like?" to get the answer notkea, how would I form that question?

You would ask Millainen lihava pelle on? Here, millainen (what kind of) asks for a description of quality, replacing the adjective notkea and moving to the start of the sentence to form the question.

Why does this sentence use notkea instead of the partitive form notkeaa?

Because the subject, pelle (clown), is a singular, countable noun. When describing a singular countable noun, the describing adjective at the end of the sentence (the predicative) stays in the nominative case. You only use the partitive (like notkeaa) if the subject is an uncountable mass noun, like water or coffee, or if it is plural.

I've also seen the word klovni for clown. Does pelle mean exactly the same thing?

They are very similar, but pelle is a more traditional Finnish word and is common in everyday speech, sometimes even used figuratively to mean a fool or a joker. Klovni is a loanword that usually refers specifically to a professional circus performer.