The C70 features 5-axis Electronic IS that works in coordination with RF lenses to provide enhanced stabilization, though it does not have a physical shifting sensor (IBIS).
Yes, by using the EF-EOS R Mount Adapter. The specialized EF-EOS R 0.71x Speed Booster is highly recommended to maintain the full-frame angle of view on the S35 sensor.
With the standard BP-A30 battery, you can expect approximately 170 minutes of continuous recording. Using the larger BP-A60 battery can extend this to over 6 hours.
No, the Canon C70 is not waterproof. It features weather-resistant seals, but it should be protected with a rain cover in wet environments due to its active fan vents.