Learn Finnish: Te yllätätte itsenne usein. - You surprise yourselves often.

It is made of the reflexive pronoun itse (self) plus the 2nd person plural possessive suffix -nne (your). When a total object has a possessive suffix, the normal object case endings (like the -n of the genitive) are dropped, so -nne attaches directly to the basic stem itse.

The dictionary form of the verb is yllättää (with two T's in the middle). Why does yllätätte have a single T in the middle, but a double T at the end?

This is a Type 1 verb, which undergoes consonant gradation. The strong grade tt in yllättää weakens to a single t in the stem yllätä- for the 'you plural' form. The double T at the end simply comes from the 2nd person plural verb ending itself: -tte.

How would this sentence change if I were speaking to just one person?

It would become (Sinä) yllätät itsesi usein. The verb changes to the 2nd person singular form yllätät, and the pronoun itse takes the singular 'your' suffix -si to become itsesi.

Is the pronoun Te strictly necessary here?