I'd like to know the current and voltage measured resolution of the products above.
Ideally, I'd like to measure voltages in the range of hundreds of mV and currents in the uA range.
The ADALM1000 uses 16 bit ADCs and when measuring voltage the range is from 0 to +5 V. Allowing for noise the smallest voltages that you can resolve is 100 uV. When measuring current the "ammeter" does not float so one end is always tied to the AWG output and currents in the range of -200 mA to +200 mA can be measured. Allowing for noise the smallest current that can be resolved is around 1 mA.
The ADALM2000 uses 12 bit ADCs and can only measure voltages directly. There are two ranges +/- 25 V which gives a 14 mV LSB and +/- 2.5 V which gives a 1.4 mV LSB. Allowing for noise you can expect results slightly worse than this.
To measure small currents you will require an external circuit to convert the current to a voltage so it can be measured. ADI make ICs specifically for this purpose, called current shunt monitors. Consult the datasheet(s) for application information. Another alternative is to use a difference amplifier to amplify the voltage across an appropriate shunt resistor. Differential or instrumentation amplifiers are a good place to start.