what is the maximum load for an instrumentation amplifier, in particular the AD620?
Pretty much all of the specifications are only guaranteed with a load of 2 kohms:



The ones where it's "otherwise noted" (for example, nonlinearity as seen in the image, and output voltage swing) generally specify a weaker load of 10 kohms, not a stronger load.

There's also this typical performance curve that shows the output drive capability falls off pretty quickly for load resistance below 2 kohm:




  I thought amplifiers are not supposed to draw any input current, except, of course, the input bias and input offset currents. Can someone explain ?


Under normal operation, the inputs will draw very little current. 

But, for example, if you drive the input voltages above or below the power supply rails, they might draw considerable current through the ESD protection diodes. You would not expect the amplifier to perform normally (give the desired gain, etc) under these conditions.

One situation where this could happen is if the driving device is powered up before the AD620 power rails are.