Will I lose Elective Monarchy if I switch to Limited Council Authority as a Muslim

It's complicated :)

If you are a count, then the succession laws for your county will apply.

If you are a duke, then the succession laws for counties don't matter to you and instead the succession laws of the duchy are applied.

If you are a king, same thing.

If you are a king, however, you can hold multiple kingships and each one has a different succession law.

If you are an emperor then that one is separate from your duchy/kingdom.

In any case, it seems that you were a count/earl and then become a duke. First you had one succession law then another one.

Gavelkind is fine for small realms. If you change to elective then you have to start giving land to your sons. If you don't have spare counties/duchies then it's not great.

It's not a problem that you lose a title to a sibling. What you can do is hatch a plot to take it back or just revoke it. Since you're probably in a small realm, the negative hit to opinion won't matter much. If you're in a bigger realm then you should go elective or primogeniture.

I believe it doesn't work that way. The title can't pass outside the realm though inheritance. But after you gain the duchy, the title will be outside of the realm, so it can stay there, even if you die.