Questions regarding the preparation and recrystallisation of methyl 3-nitrobenzoate
Answer 1 - you want to keep the whole reaction cool, preferably below 6 °C, because the nitration reaction is exothermic. If it gets too hot you will lower your yield due to side-reactions. There is also the possibility of runaway reaction degrading the starting material and product. This is why you don't heat it.

Answer 2  - someone somewhere has done the comparison crystallisations and determined that EtOH is a good solvent for the recrystallisation. It is also cheap and safe for students to handle.