All the three factors are true, albeit at different degrees:
1) Italy is one of the countries with longer life expectation, and very few new born, so the average age is very large. We are an old country... But Japan has exactly our same age profile, and they had much less deaths! So this is not the dominant factor.
2) We are reporting as CV-related all deaths of hospitalised patients affected by CV. CV is actually quite often the additional problem causing the death of people with pre-existing diseases, but who could survive also several years without being infected by CV. Hence I think it is correct to consider the CV responsible of their deaths. On the other side, a significant number of people die at home, without being tested, and hence they are not counted as CV-related. On the average probably these two factors balance out, hence this is not causing a significant over-estimation.
3) Definitely the number of infected people is grossly underestimated, as we do not have the same testing capability as South Korea. Only people being hospitalised with significant symptom are tested, simply because we are unable to test also people with mild symptoms, or asymptomatic but living together with infected people. This leaves a number of infected people going around and infecting others. It would be necessary to perform massive tests involving all the population potentially exposed, and quarantining all the infected, but we are not equipped of the proper testing facilities, as instead South Korea managed to provide.
The other countries should learn from our errors, and from the success stories in SK, Hong Kong and Singapore, where widespread testing and tracking of infects managed to avoid the massive spreading of the infection we have got here.
Unfortunately I do not see those proper policies being applied in other European countries or in the USA...
I suppose that all them will follow Italy's route, instead of South Korea...