Hi,
The CC2570/71 is a network processor only which is why information such as flash or RAM is not available, and at the moment TI does not yet offer an ANT System on Chip.
The lowest power mode on the CC257x is Powered Down Sleep, so the sleep mode current is 0.5uA. In-between ANT messages on a synchronized master/slave channel the current is 1uA. There are more detailed power measurements about a CC2571 based module here.
ANT supports 80 RF channels; BTLE breaks up the 2.4GHz spectrum into 40-2MHz channels, while ANT breaks it up into 80-1MHz channels. ANT does not define these channels for any particular role, so any RF channel can be used for any type of data. As with any wireless protocol though if you using multiple RF channels you should try to keep them reasonably spaced apart to reduce any side-band interference.
An ANT master channel doing broadcasting and a BTLE slave doing advertising are different conceptually. An ANT master channel broadcasts into a timeslot which any number of ANT slave channel devices can synchronize to which allows both ends to save power and provides bi-directional communication. ANT masters automatically detect interference in their timeslots and adapt accordingly which allows multiple masters to co-exist easily. BTLE slaves are allowed to advertise into up to 3 different RF channels, but the BTLE master will have to scan to find these advertising packets quickly which can be costly power wise depending on your scanning interval and length settings. BTLE then encourages you to go into a master/slave mode to save power and deliver bi-directional communication, now at the cost that the slave is no longer free for any other BTLE master to connect to (the BTLE master will automatically take the slave to a different data RF channel, period, message length, etc).
You can check out this page or this thread for a brief summary on how ANT operates, and when you start testing feel free to visit the thisisant.com website on how to get started.
The 1 and 8 channel limits on the CC2570/71 respectively are with regard to how many standalone synchronized master and slave channels you can have open simultaneously. You can open and close these channels as either master or slave dynamically no matter if others are open and with different channel parameters. Both devices still support continuous scanning mode and shared channels if you have a bi-directional many to 1 or 1 to many topology.
BTLE does not set limits on the number of synchronized channels in the specification so it's up to the vendor to define this number. Anecdotally I've heard the CC2541 in master mode can service up to around 3-4 BTLE slave devices before it may begin to hit some operational limits but there are always firmware updates and such so I would test that for yourself :)
Actually since this is now announced, there will be changes (not sure when the release date will be yet) to the ANT Radio Service to allow concurrent applications to run in the background by dynamically sharing available ANT channels so multiple Android apps can stay connected to multiple devices, which might be handy for your use case if it needs to stay connected to the phone 24/7.
Sorry if it got a little wordy there!