HPS bulbs and ballast wattage compatibilty vs replacement technologies
1.  With HPS, no for smaller bulbs on bigger ballasts.

Discharge lights are current devices. They are non-linear (behave almost like a dead short)  and so, must be externally current-limited.  That's the whole point of a ballast or driver.  

HPS bulbs work at a specific current in one of four working voltage ranges (page 9): 52V, 55V, 100V or 250V plus or minus 15%.  To swap, the bulbs would need to be in the same voltage range.  Too small a bulb, the bigger ballast would force the higher current through the bulb, burning it out.  The reverse, the bulb might work, but might not warm up properly. 

By comparison, if you stick a VHO 8' fluorescent tube in an HO fixture, you get HO light output from the VHO bulb.  

2. Nope! Different and incompatible, especially ignitors

You absolutely cannot interchange various types of discharge lighting - not least because the way the ignitors work is very different.  

Here, HPS is an odd duck.  It has an ignitor which fires a 2000-3000 volt spike to ignite the bulb. The supply is constant-current, so it will increase voltage under no load.  This triggers a VBO, which flows a burst of current into a winding on the ballast transformer, inducing a spike to the bulb.

They make special MH bulbs made to run on HPS fixtures; these are resistant to the spike and are tuned for HPS voltage and current. They cost 50-100% more than a stock HPS or MH bulb. 

Other than that, facility managers don't intentionally use the wrong bulb.  Nobody will support that, so if you want to try it, you're on your own.  It will either not work, give poor life, burn out the ballast, or blow bulbs - and these suckers run very hot and you don't want molten sodium raining on your head.   Some are even reputed for starting fires. 

3. LED replacements must be designed for that.

You linked a compromise screw-in LED meant to go into an HPS or other HID light without removing the ballast. If they are designed, (UL) listed, and labeled for that use, it's safe and legal.  Otherwise, it is not.  The operative word is "compromise". 

HPS is more lumen-efficient than any but the most efficient LEDs on the market - if you like yellow light.  And if you're trying to light the inside of a sphere, which you might if you're growing pot.  Reflectors suck. If you really want a cone of light (and most people do), LEDs win big, because they inherently emit a cone of light.  They are far more lumen-efficient inside that cone, and weak reflectors don't help enough.

Of course, if arranged like a "corn cob", the advantage is utterly lost.  SMH... Those are for people in a hurry looking for a screw-in replacement that uses their same reflectors and lensing.  But wait.  Why keep the old fixtures?  Do you really want to keep the old ballast?  No, it wastes energy and is a maintenance item.  You want to direct-wire existing line voltage to the LED device. Do you honestly foresee rolling back to actual HID lighting?  Never gonna happen.  Throw the fixture in the attic, get a modern LED fixture for 1/3 the cost - and don't look back. 

Standard practice is replacing a 400W HID with a 6-tube F32T8 fixture. 4' LED replacement tubes are a commodity item, and prices are in free-fall -- $8 last I checked for a top brand. $48 and you have a HID light's worth of LED light.  Hit up Craigslist for a used fluorescent fixture, yank the ballast and rewire direct - you're in business. Given how cheap LEDs have gotten I wonder why anyone would fool around with HID lighting anymore. 

Real fluorescents are even cheaper if you get eBay ballasts, and the superb tubes now available.