Are we allowed to use olives on Rosh Hashana? Also, I know we don’t use nuts, but almonds for example which are called Shkeidim and not officially Egozim, can we use?
There is no problem to eat regular olives. Olives in vinegar, however, should not be eaten.
The Poskim mention not to eat nuts because they increase saliva and disturb our Davening, or because אגוז – Egoz is the numerical value of חטא – Cheit. Almonds too increase saliva, even if they are not strictly Egozim. Note that the Makor Chaim writes that Luzim which are not to be eaten on Rosh Hashana are Shkeidim – almonds. Ground almonds in a cake are okay.