Hi Thibeau,
Unfortunately I don’t know the answer to you first question, but I can adress your second question.
I believe the brackets {} are used as shorthand notation for an integral. Compare for example the first and second expression on slide 14. You will notice that {3x_1y_1} is shorthand notation for the integral over dr_1 with as integrand 3x_1y_1*rho_1(r_1).
I hope this helps.
Best,
Stijn