Yes you can. It is considered a fairly minor procedure that should not effect your sex life at all. After initial recovery you will be able to have sex normally with no issues. Even with a double orchiectomy you can still have a completely normal sex life by undergoing testosterone replacement.
Yes you are quite capable of having an organism after the surgery. In truth the most common side affect is more mental than physical. Now if you are having trouble getting aroused consider getting hormonal theraphy. Similar to what women undergo after they enter menopause sometimes.