You don’t have to repeat the word “pour” in the second sentence.

The word “aussi” is correctly placed.

There are a number of ways you can improve the overall sentence however, avoiding repeating twice the word “pour“.

Also, instead of using the word “aussi“, you could consider using the word “également“.

One way to go would be, for example:

“J’utilise mon portable afin d’effectuer des recherches. Je m’en sers également pour bavarder avec mes amis et contacter mes copains.”

Along with Von Kar said, it all depends on the language level you want to use.

As far as I’m concerned, your sentence is well formed and suits an oral discussion.

However the accumulation of ‘pour’ is obviously unsuited to written expression, where you’d expect a higher sentence grammatical and syntaxic complexity.