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I am Indian and have a multiple entry Danish business visa and they have requested me to give the itinerary for 16 days even though I have applied for a multiple entry visa.
And do I need to apply for a tourist visa even after having a multiple-entry business visa?
Generally speaking Schengen visas are valid for all allowed purposes (there is no “business” or “tourism” category like in the US for example) and for all countries in the area. So if you really do get a multiple-entry visa with a long validity, it's fine to reuse it for another purpose after your first trip and you don't need to apply for another visa if the first one is still valid.
Single or two-entry visas are a bit different in this respect, see Can I use my Schengen visa for a completely different purpose and entry point? and Can I travel to Spain using a Greek Schengen visa even if I don't want to stay in Greece at all?.
Do note that even a multiple-entry visa might not offer much flexibility as you also need to follow the rules on maximum stay and visa validity.
Now, usually you would submit an application and the consulate would decide what to issue depending on that and on your past history. So it's somewhat strange that they would already have decided they will issue a multiple-entry visa before seeing your itinerary and that they would tell you how long your trip should be (are you sure you got that right?). As your subsequent experience showed, consulates can always issue what they want and you won't be sure before you have the actual visa in your passport.
In any case, when applying for a multiple-entry visa, you only have to provide proof of insurance for your first intended trip. You can get insurance for any subsequent trip later.
