I am a math undergraduate in my second year. I was thinking of applying to internship but I am confused about this. 1. Is it okay to apply to more than one professors at the same time? If so if I get selected in more than one and I consider only one will that affect my reputation with professor badly? If so how can I avoid it? 2. Will it be okay if I try to apply in two fields of the same subjects? I am kind of inexperienced in this; so any help would be appreciated. :)
User Karl has good advice, I will only add that if you ask two professors for positions, make sure that you at least hint that there are other possibilities under consideration. If you indicate that you would take an internship with a professor while you are looking for another, it might cause hard feelings later.
But if you present it as "I'm looking around for opportunities for an internship and wonder ..." then it doesn't immediately sound exclusive. If you get more than one offer you then have a comfortable way to go back to the ones you aren't taking with an update. "Thanks for the opportunity, but ..."
Keep your lines of communication open as much as possible.