9 (7.4v) Li-ion rechargeable battery maximium drain current?
No, it is wrong to assume that every Li-Ion battery has 10C discharge rate. As a matter of fact, only specialized batteries for Radio-Controlled toys have high discharge rates, 10C, 15C and above. Or industrial automotive/bike batteries. Most batteries that are designed for long-term operations (as smoke detectors) use more conservative design materials, thicker membrane separators, etc. and are optimized for low discharge rates. 

Looking at the battery, it seems that it has an actual capacity of about 550 mAh, and voltage 8.4V (2 Li-Ion cells is series, typical). I wouldn't charge it at more than 200-300 mA. 

The charger, however, reads "8.4 V 500 mA" as per customer's questions-answers at Amazon, which implies the use of ordinary USB port. And the marketing materials say "charges 3 batteries in 3 hours". This leads to the following calculations/speculations. 3 hours with 8.4 V at 0.5 A is just 12.6 Watts-hours. Which means (assuming ideal converter) that each battery has the capacity of 4.2 Wh. At 8.4 initial volts (and likely 7.6 running volts) it makes the battery capacity as about 550 mAh, which is likely it's real capacity. So, I would say that the discharge rate of about 55 mA is the right one for this battery.  You probably can get more, 200-500 mA, but the capacity will degrade.

EDIT: From some reviewers, this "9-V" battery is the best, made by iPowerUS. Here are test data for it. Discharge current is 500 mA max. Internal resistance - under 450 mOhms.