Should one wear shoes for tefilla? If so, are slippers sufficient?
If it is permitted for some parts of tefilla and forbidden for other parts of tefilla, please specify? For example, forbidden for the amidah but permitted at other times.
Is there a difference between men and women? For example, forbidden for men but permitted for women.
It is definitely more respectable to daven with shoes on, in a respectable befitting manner for talking to the king! There is a special halacha that we should prepare ourselves for the meeting with HKB”H Himself. Now although this is what is the correct thing to do. It is halacha only in regard to saying Shemona Esrei. The halacha is that when we stand Shemona Esrei, we are to be dressed the way a person would be dressed when greeting an important person, or at least the way we would go outside in the street when we are going somewhere. If the norm in your area is that you would not be dressed this way for one of the above things, then you shouldn’t wear slippers etc. however if we would go outside dressed in such a way, and it is acceptable in your area to do so, then it would be permitted.
These halachos would apply for anyone davening Shemona Esrei, men and women, that they shouldd be dressed when davening Shemona Esrei the way they would dress when a respectable person would come to the house.
O:CH 91-5, M:B 11, Piskei Teshuvos 91-4 ftnt. 32