Well, i notice that if i send a SMS too fast before my phone show that the previous one is sent, my phone will say something like "Still sending previous".
1) Well, does the speed of sending an SMS ahs to do with the build in modem of the phone?
2) And does that means that there is a maximum limit in the total amount of sms a phone can send in one day (24 hours)?
3) If the speed of sending sms depends on the builde in modem, is there any nokia phone which can support higher speed?
Phone modem does not effect this that much after all, SMS messages are being sent on signaling channel and that is usually the limiting factor.
You can speed up the SMS sending by disabling delivery reports for example. I have never tested the absolute maximum message amount per certain period of time, but I would say that one message per 10 sec would be the optimal value.
For higher speed you should ask your operator if they can offer you a direct communication to their SMSC over some different protocol, like CIMD2.