No response after application

Hey everybody, I am in 2nd year masters in Italy and just started to send applications for intership. I just sent couple so far in february-march. I applied in the first days as applications were open to some of the biggest instutions here. To this day I have no answer. I am new to the applications game so I would like to know if big, reputable instituions always send you the outcome of application process or it also happens that instead of rejection they just ignore it and dont inform you about the rejection. I would like to know it since in case of rejection, I have contacts for couple of people from the HR departments that I met on my uni stage days an in case of rejection I would like to ask them what to improve etc etc. but idk if I should do it just yet since I have no asnwer so far so I dont want to embarass myself in case that application process is not finished yet. Thanks in advance.