Anybody can explain me the reason why: -we don't say 每个年 but 每年? and, on the contrary, we must say 每个月 and not 每月? -Is there somethig to do with the fact that sometimes we must use 全 (全身)instead of 整个 while we must say 整个身体 and don't 全身体? Thanks (Húli) PS/Afterwards I have introduced some changes on my previous post in order to clarify it.
The reason is that 天, 日, 周, 年 are themselves counter words / classifiers (so they don't need an extra one), while 星期, 礼拜, 月 are not classifiers and therefore require a classifier, which happen to be 个 for the all of them.
Note that although 月 is listed with the ones that require a classifier, it's quite frequent to hear 每月 as well (which I believe makes sense since we already have a classifier for day, week and year).
The rule is: 天, 日, 年 do not take 个 as counter word.
一个星期，一个礼拜, BUT: 一周 goes with no counter word. All of these mean 'one week'.
一个月，五个月, BUT: 一月 is January, not 'one month'.
I'm Chinese, I never say 每个年, but i do say 每月 sometimes (for abbrev).
and I never say '整个身' or ‘全身体', I do say 全身(describe physical) or 整个身子(describe physical) or 整个人(describe mental more)
全身湿透了(wet through)，整个身子都受伤了(injured everywhere)，整个人都不好了(not feeling well).
correct：一天(one day, whole day, depends on context)，每天(everyday)，一日(one day)，每日(everyday)，一个晴天(a sunny day)，一个星期天(a Sunday)，一星期天(the whole Sunday, '一' means 'whole' in this case),一星期(the whole week),一年（whole year），一个闰年
wrong: 一个天，每个天，一个日，每个日，一个年（maybe correct in some case），一晴天（this one could be correct in some rare case）
some case: 纸上写着一个年(字)。 我们不知道失去了母亲的他这一个年是怎么过的。
rare case: “我当时就纳闷了，这一晴天，他打着伞干嘛” this maybe happens in Chinese crosstalk (xiangsheng) or talk show.
As a native speaker, I don't suggest you to memorize those things as rules. because there are toooooo much. Even though you use the wrong one, you are still correct from the perspective of descriptive grammar, as long as we can understand what are you talking about.