C’est le garçon auquel je pense

Yes, this is correct.

C’est le bœuf duquel je parle

This is incorrect. “duquel” may be translated as “from who/which”, so you should is it in a sentence like this:

Je parle du pays duquel tu es né

Note that the use of « duquel » is very rare, and seems to be formal. On an oral conversation, I would not use it, I would change the structure of the sentence to avoid it.

Il est le professeur dont je parle

The usage of “dont” is good, but the beginning is odd. In french, you don’t use “il est” when you are describing a person, you will use « c’est », or « c’est lui »:

C’est le professeur dont je parle
C’est lui le professeur dont je t’ai parlé

Using « c’est lui » emphasis the fact that you are talking about THIS person in particular, and not an other one.