一年有多少天 is correct.
People would prefer to use 多少 if they know the number is greater than 10. 几 is used mainly when we already know the number is less than 10, in which case you can use 多少 as well.
As well as 天，年 is never preceded by 个. However, we often say "...个月“. Note:
几个月 = how many months
三月 = March
三个月 = 3 months