Reverse voltage protection for lithium battery charging module with smd component(s)

Question

I want to add to this famous single cell lithium ion battery charging module a reverse voltage protection:

I ended up with the following circuit (Load draws up to 700mA):

Updated:

My question(s):

1. Is this already enough, or should I add a Zener-diode/transistor, etc. (if yes which one - SMD is preferred)?
2. Is this one p-channel MOSFET able to switch fully on, even when the battery is almost empty (2.9 V) or would another fit to this circuit better - SMD preferred?

I've found a lot of solutions out there, but either for 12 V-stuff or oversized.

Answer 1

Is this already enough, or should I add a zener-diode/transistor etc

It would be enough if you had the FET wired correctly. You need to swap the Source and Drain so the body diode doesn't conduct with reverse battery polarity.

Is this one p-channel mosfet able to switch fully on, even when the battery is almost empty (2.9V)

Yes. But you know this already because you read the datasheet, right?