Response to Question 1
In low power applications, mAh helps determine the battery life. When determining the battery life for an application the mAh advertise in battery specification sheet is important, but more importantly how the mAh are derived. Different regions in the world use different criteria to determine the mAh. For example USA markets will use around 20mA load to derive the mAh for a battery where as the same manufacture will use a 30mA load for outside of USA. As a result the same battery will be listed as 1500 mAh battery for the US market and 1400 mAh for markets outside the US. Therefore if mAh is important for the application a dialog with the battery vendor will be very beneficial.
Below is a discharge curve vs service life chart for a Duracell Ultra 223 CRP2 battery.
From the above chart it note that the service life varies based on the discharge current. Therefore it is important to review the specification sheets to understand the battery capabilities as it relates to the specific application.
Response to Question 2
Technically there is no resistor inside the battery, but components use in battery contribute to a total effect resistance, also known as internal resistance. The two primary contributing components are electronic resistance and ionic resistance. Electronic resistance is made of material such as metal covers and material used to make contact. Electrochemical factors such as electrolyte conductivity, ion mobility and electrode surface area make up the ionic resistance component. Ionic resistance occurs slowly and effect on effective resistance varies base on various factors.
Note: CR-P2 batteries are made by combining two CR123 batteries.