In order for me to transport passengers do I need to build passenger terminals?
No, the AS-Handling-Company will take care for your passengers and you have to pay for the service provided by AS.
You should think about own terminals only in case you have a bunch of money and you to not know how to invest :)
Terminals are part of a flight's rating, as well as your cost. AS passenger handling is AS$11/passenger, and provides a two star/bar rating. By building a terminal, you can save the handling fee and increase the terminal rating for a flight. However, the cost involved in building a terminal is very high. Most players won't bother.
As an addendum, cargo handling is AS$25/unit, and building a cargo terminal is significantly cheaper than building a passenger terminal.
Thanks for the help guys 
Though I accept all the above, it may be worth the investment for some particular high yielding routes that have a lot of competition.
For example, flying LHR - JFK, your terminal may just be the one to fill up the planes, in particular with business and first class.
Saad
Silly question. Does building a passenger terminal increase the number of slots available at an airport or are slots limited to runway capacity (as per real life)
Doesn't affect the slots in any way.
The capacity you set? what happens if you have more passengers then your terminal can handle what happens then?
AS will take care for the passengers and you have to pay AS handling fees.
When you build a terminal the connect time between flights(MCT) in this same terminal is reduced?
Regards,
Carlos.
No...