The visa will have an exact start and end date. You don't have to enter and exit on exactly those days, but you can only enter on or after the start date and leave on or before the end date. So when you apply for your visa put the earliest possible date you will be in Russia and be sure to get a duration that will give you plenty of time.
If you plan to go into Kazakhstan or Mongolia (Mongolia free 90 days on arrival for Americans by the way) then you will need to apply for a multiple-entry visa which is much more expensive and a little bit more complicated. However your visa will just say "Multiple Entry" and will not have any specific dates that you have to be out of Russia during that time.
Don't know about the hotel voucher. I did not need one but I applied with my UK passport both times. In any case, a fully-refundable hotel booking in Moscow (cancelled once the visa has been issued) should suffice.
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