Will the MAX40200 output be stable with an output capacitance greater than 100uF?

Yes, the MAX40200 will be stable with an output capacitance greater than 100uF. The output does need at least 0.33uF, but there is no upper limit on the output capacitance. The datasheet lists the spec from 0.33uF to 100uF. The reason 100uF is listed as the maximum is because of inrush current. With a large output capacitance, inrush current through the MAX40200 will also increase. Too much instantaneous current can damage the part. So, the datasheet spec caps it at 100uF to be safe.

Can the MAX40200 be connected in parallel to support 2A output current?

Due to variations between devices, there exist differences of the on-times and forward voltages between two diodes. When connected in parallel, if one diode conducts first, then all of the 2A current may flow through a single diode, thereby possibly causing damage.

Can I leave the EN pin floating on the MAX40200?

Yes. The EN pin has an internal weak pullup and can be left open for normal operating conditions.

What is the MAX40200 maximum current?

Can the MAX40200 handle continuous 1A current reliably? This device is available in SOT23-5 and WLP packages. The WLP package can handle more current as compared to the SOT23-5. The absolute maximum current that can flow between VDD and OUT is 1A and 1.2A for SOT23-5 and WLP package respectively. Please also bear in mind that this is the absolute maximum and not a rated specification. As a rule of thumb the rated specification can be taken as 20% below the absolute maximum rating. So, yes, the WLP package can handle continuous 1A current but the SOT23-5 can't.