[Strong Letter or Experience]

I have two options for a summer internship. One is a reading project with a professor at my university and who has a good impression of me, even though I didn't take any of his courses. I am very confident that he'll write good LOR. Other option is an internship at one of the top research institutes in my country, with a professor I don't know. I did some research and found that the second prof is very chilled and also might write a good recommendation. But the subject in which I am doing an internship (at the top institute) is not really my strongest but I'll have an amazing thing to put on my CV, if I did. 

 

What should I do ?

[Should I apply to grad School in Applied mathematics with physics background]

I am in Bsc Math and Physics programme. I have taken mostly pure math courses [ like Algebra, Analysis(3 courses), calculus, differential equations, topology, complex analysis, probability ]. I wanted to msc in applied mathematics and will apply during the fall this year. I want to know whether I even have a chance if I apply. Can someone provide some perspective ?

[Shifting from pure science to applied science/mathematics]

I am a second year undergraduate in Pure Math and Theoretical Physics. I have decided to study applied mathematics or applied physics in grad school.  Does anyone have a similar experience? 

In particular, I would like to know 

1.I have not taken any applied science/mathematics courses till now. I am planning to take them next sem onwards. Is it a bad thing on my application?

2. Does having a theoretical background, put me in a "This guy can't succeed in applied stuff" position ?

3. When someone shifts subjects, what exactly does the grad school expect in the application, other than relevant coursework and grades ?