Should I ask for each recommendation letter separately?
I would recommend that you do not send a group mail to professors you plan to ask for help. It will look somewhat lazy, and some may be offended that you were not willing to take the time to write a separate email (which should barely take any time). Another reason why this is bad is that hopefully each recommendation will not be saying the exact same thing, and you may want to reflect differences when you ask for the letters.

In fact, I would probably recommend approaching the professors (or others) that you plan to ask in person first. Of course, this depends on your relationship with the professor-- if they are very busy and have already previously agreed to write a letter then this step might not be necessary. However, when asking professors for letters it might seem a bit impersonal if you do not ask in person, and you also will not be able to gauge their reaction to be asked if the correspondence is online.