SIM900 and Mega 2560 not sending SMS
I was just able to send an SMS (even with the 1A supply). Here the answers to my questions.


No, it is not necessary to flash the SIM900 board
I was not connected, because I didn't insert the SIM card properly on the shield.
No it does not necessarily need 2A for logging into network and obviously not for sending SMS though there might be reasons for the board consuming 2A during SMS sending, e.g. bad network connection.
If you want to use Sotware Serial, you need certain digital lines allowing software interrupts. In the case of the MEGA board, e.g. D10, D11 or for the UNO D7,D8. 
I was using this tutorial to get communication via SoftwareSerial working. Afterwards I added the code for sending SMS.


I hope I can help some others who are looking for a low level description of how to get started with MEGA and SIM900.