Letter of recommendation

I've just graduated in Brazil and I plan to apply in some different Master courses in US. About the letters of recommendation:

-should it be specific to the university I am applying to? I plan to apply to different universities and I did not want to ask my professors to write many different letters. Can I use a generic letter to all applications?

-should it be written and signed in paper or digitally? Since I plan to send to more than one university it was better to send a digital copy (signed digitally). Otherwise I would have to ask for many signed copies. Universities in general ask for digital or physical letters?