The history books will record the names of the Russian athletes as the individuals who won their medals. They will be recorded as “Olympic Athletes from Russia,” but their medals won’t count towards a tally for the country Russia. At least that’s how I understand it.
As far as how many spots for Olympic Athletes from Russia, the IOC stated that the qualification will be through the ordinary Olympic qualification process for their sport. I assume that means Russian ladies keep their 3 spots, and the athletes will be decided through the normal Olympic selection process, i.e. selection by their federation. This isn’t confirmed but it seems like the most likely assumption based on the IOC’s wording.
Based on this, I don’t think we can have more than 3 Russian ladies at the Olympics, since only 3 spots were qualified through the normal process, but if Russian ladies go, they’ll be the ones chosen by the RusFed, not by the IOC.