The Moisture Sensitivity Level (MSL) is a measure of how much, how fast, and how sensitive a part is to moisture before being attached. It has nothing to do with moisture sensitivity after the board is assembled, for such information you need to consult the datasheet for storage and operating conditions.
If too moisture much enters the part and it vaporizes during reflow, the high pressure can cause sufficient stress to cause the part to explode, causing a "popcorn" noise. Such failures are usually visible with careful inspection as the package will be fractured, usually near the leadframe. It may be cracked on the bottom with DFN-type packages, however, though the device may appear to be sitting at an odd angle, canted up from the PCB.
Depending on the device, other, more subtle failures may occur. Internal wire bonds could be broken causing intermittent or no connections, or in the case of a PPTC, an effectively reduced current limit. Such errors are probably rare, and of course very dependent on the construction of the device, which you don't know. For prototypes, usually people can deal with it, but for production it's important if you are concerned about reliability and/or manufacturing rejects.
You can keep moisture-sensitive parts in resealable containers if you control the humidity with desiccants or dehumidifiers, and you can use indicator cards to monitor that the humidity did not exceed some defined level. 3M makes them, and there may have been one in the bag from your supplier.
If you do end up with a big production batch of moisture-sensitive parts that have been exposed, you can "bake" them to drive off the moisture. Check with the manufacturer, but bakes can be anywhere from 40 °C at 0% humidity for 1-4 weeks (gentle, but complicated), or 125 °C for some number of hours (more aggressive, but your parts may or may not like it). If you're just making prototypes for development...just make some spares (as one does anyways) and fuggedaboutit.
So for polarity reversal causing no damage and requiring no fuse replacement you can use pretty much whatever diode you want and put it in series so that "normal" current flow passes through the diode only if properly plugged in. With the current requirements and voltages that you're working at, this shouldn't be an issue. A simple silicon diode should be fine.
For overvoltage you're going to want a circuit more like what Nick Alexeev suggested in the comment. Essentially a zener diode with a PTC or other type of fuse. The Zener should have a value which is less than the maximum input to your regulator.
So basically, if you reverse batt_in+ and batt_in- the first series diode will prevent any current from flowing and protect your circuit. If batt_in is greater than the breakdown voltage of the zener, it will start pulling down a lot of current, and blow the PTC fuse.
The only extra thing you might do, is to guarantee that the startup current doesn't exceed your PTC's current limit, you can place a resistor on "protected V_IN+" or "protected V_IN-" (in series before the regulator and decoupling capacitor) such that:
(BATT_IN+ - V_forward_diode - Resistor*Maximum_expected_load) >= Vmin_regulator
For the desirability of any specific characteristics for the PTC, the diodes, and everything else, it all depends on your application. In general, I tend to wing it unless I have a real reason to crunch the numbers. I'm also a bit too tired (on my way to bed) to really get into how to calculate what these values should be, but if you need this info ask in a comment and I'll post some tips on getting the numbers.
Though, why not just use a polarized connector for the batteries so that you don't have to worry about whether the connector is plugged in backwards? And in what context are you going to overvolt? Think about these questions too when trying to answer a more complicated design choice (a polarized connector is easier than adding an extra diode, and is less likely to lead to extra design considerations).
Hope that helps!
Best Answer
These fuses are not precision devices. The nominal ratings are at room temperature and reflect the difference between the current the device is guaranteed to carry vs. the current it is guaranteed to open at (after some unknown delay or specified delay). You generally cannot actually use the device near the lower rating, nor can you assume it will open at the higher current within a reasonable length of time. They're just rough guides.
To determine how these things behave you need to refer to manufacturer's data. In the case of the RUEF300, nominally a 3A device made by Littelfuse we have this specification sheet and this catalog/datasheet. Other devices using the same principle will behave similarly, so take this as a representative sample.
From the first one we have this snippet:
Our nominally "3A" fuse is guaranteed to carry 3A @20'C and guaranteed to open within 10.8 seconds when carrying 15A. That's a 5:1 range.
The 6A trip current rating here has no time specified, but it is certainly more than 10.8 seconds that the 15A applies to.
But we have not even taken temperature into account yet.
So if our board gets hot, we may not be able to count on our "3A" fuse to carry more than about 1.5A.
The current to cause trip within a fixed time (10.8 seconds) will go up from the maximum 15A when the temperature is lower than 25'C.
There are other imperfect aspects- the interrupting current is 100A DC/70A AC, so it may not open properly if the fault current exceeds that, and the maximum voltage is 30V, so the open voltage should not be allowed to exceed that rating.
They are basically thermal devices so they require a significant voltage drop to open, which may affect your circuit.
Finally, being thermal devices, the mounting can affect the trip current. It's more important with SMT devices, but if you were to, say, pot the through-hole device described above, the trip current would increase.
As @MichaelKaras points out in the comment, the devices "wear" and characteristics change every time the device trips. The specifications are for a new device. From the IEEE paper Failure Precursors for Polymer Resettable Fuses the below graph shows the change over operations for some typical samples. Resistance also tends to increase with number of operations.