Is there any way to follow my favorite questions to get notifications (answer, comment) to my messages inbox such as the question I asked?
If there is not, could you add this feature?
There's currently no way to get notifications for favourite questions (starred questions). You can mark favourite questions like this:
The 'favorites' tab in your profile will show you any activity on your favourite questions — the number on the tab increases, like this:
Images from Meta Stack Exchange's FAQ on favourite questions.
You don't get an inbox notification, but when you go to your profile and check, this will be indicated. When you click on the tab, the questions with recent activity will be near the top, and highlighted in yellow.
There is a request to add notifications for favourites, but that was nearly 7 years ago, and it's still not implemented today. So, unfortunately, this seems unlikely to happen, and you'll have to use the alternative method I described above.