No, the FS700 records 1080p internally. To record 4K, you must use the 3G-SDI output connected to a compatible external recorder like the Odyssey 7Q+ or Atomos Shogun.
The FS700 can capture up to 240fps in Full HD (1080p) for an 8-second burst, and up to 960fps at significantly reduced resolutions.
It uses Sony L-Series (NP-F) batteries, such as the NP-F770 or NP-F970, which provide several hours of continuous operation.