Using a Dual Bidirectional I2C Bus Voltage-Level Translator
1: current draw is very small, basically just what's needed to run the I2C bus. look at the pull-up resistors, that's pretty much it. In any case the 20mA limit does not apply to the VCC pins on arduino, than can provide more current.

2: there's the Adafruit level converter, it's basically the same thing done using discrete low-power MOSFETS, unlike the TI chip I don't think it can operate below 3.3V, but you don't need that feature.

https://www.adafruit.com/product/757

this is the NXP application note behind the adafruit logic level converter. https://cdn-shop.adafruit.com/datasheets/AN10441.pdf