delete the memory or re-upload a program
How do I know, how much storage capacity is available on the Arduino board before and after I uploaded something?


In yellow is how much bytes does your program take.

In purple is how much bytes are available on your board.

In green is how many bytes does your global variables take.

In orange is how many bytes are left for local variables.

In blue is how many bytes are available for all of your variables.

In red is the general specs of your board and to which COM port it is connected to.






  How can I delete a program from the Arduino board?


Once  a new program is uploaded, the old one is deleted (somewhat). Still, you get all your bytes back and it is like if you start from scratch




  When I upload a program, will the program that is already on the Arduino been overwritten?


Yes.




  Is an Arduino generally used to execute one specific program and not to hold a set of totally different programs?


An Arduino can only execute 1 program at the time. It doesn't usualy hold on to any other programs, but can store 1024 bytes in it's EEPROM. This lets your write in the EEPROM with a program and access that data with an other.