No.
They get a free grapple check with a +4 bonus when you try to place them into a hazardous location. Not "so long as they're in a hazardous location and being grappled". Effectively, if they weren't in a specifically hazardous location before, and they will be after, then and only then do they get a free check. Moving them around while keeping them held them in a wall of fire is fine.
As such they certainly don't get a check every turn you move them anywhere above the ground. When do they get a check? It depends on what is accepted to be a "hazardous location".
Being carried off into the air is a hazardous location
This is fairly reasonable. Even if you're not actually going to take damage from falling, a mere 5 foot fall is likely to be inconvenient and possibly indirectly harmful (you could fall prone at the very least - that's a hazard). Regardless, being in the air arguably just hazardous because you're not supposed to be up there and can't move around normally or get down. Even if you don't buy this somewhat weak justification, doing it this way helps to avoid the weird corner cases of the second interpretation.
If this is true, then they get a free grapple check when you try to lift them off the ground. Specifically, when you move them 5 or more feet above the ground; moving them around less than 5 feet above the ground probably doesn't actually count as movement, even if that their feet are described as being off the ground due to your wrestling moves or whatever, because you can't move in less than 5-foot increments¹.
Being high enough above the ground to take falling damage is a hazardous location
This one is also fairly reasonable. If this is true, they get a free grapple check when you try to lift them high enough that you can cause them [falling] damage by letting go. By this logic, holding them over, say, a pool of acid would also grant them a free grapple check. It's just as hazardous a location as being held far above the ground, and for the same reason - they'll take damage when you drop them.
What if they won't take damage from certain falls? What if they have an extraordinary ability to reduce falling damge? Or what if they'll be falling 20 feet, but it's onto some very soft mushrooms that will cushion the landing and prevent all falling damage? They probably don't get a grapple check, but the rules are unclear.
Falling is a hazardous location
Under this interpretation, it doesn't matter how inconvenient or potentially dangerous the location is. Unless it is actually immediately² causing you damage, it's not hazardous. This also makes a certain amount of sense. They don't get a free check if while grappling you move them into a location where they're being flanked by a rogue, after all, even if that is arguably exposing them to a bunch of extra sneak attack damage.
If this is true, they get the free check when you let them go, regardless of how high you are flying (except they probably don't get a check at all if they're only 5 feet up and wouldn't be taking damage anyway). The issue with this (as mentioned in comments) is, well, this grapple check is only going to harm them. It's a free check to break the grapple. If they break the grapple, they fall anyway.
It also seems to contradict one of the examples given in the text ("when you place your foe in a hazardous location, such as [...] over a pit"), which strongly implies that it's one of the first two interpretations that are correct.
¹I don't know if this is explicitly stated anywhere.
²Meaning "before you get a turn"
By RAW, probably.
Here's the relevant rule (PHB, p. 290):
If multiple effects impose the same condition on a creature, each instance of the condition has its own duration, but the condition’s effects don't get worse. A creature either has a condition or doesn’t.
For example, if a creature had the paralyzed condition from both a hold person spell and from the effect of a ghoul's attack, saving against the hold person effect wouldn't end the paralyzed condition until the ghoul's effect was also saved against.
So as long as your DM agrees that your two grapples are separate 'effects', there's nothing in the rules that seems to prevent you grappling the same creature twice. The creature would need to break each grapple separately (per the rules on PHB. 195 for "Escaping a grapple").
However ...
Your DM might quite reasonably rule that, absent other rules, a grappling character (rather than a grappling limb of a character) constitutes a single 'effect' for the purpose of imposing the grappled condition. If so, then you can only impose one grapple on a given creature.
Best Answer
A creature can be grappled by multiple creatures, and it has to make a separate escape attempt against each one.
There's nothing in the Grappled condition that would prevent multiple creatures from grappling a single target.
Where it gets complicated, though, is breaking free. From the grapple rules for monsters, we have this:
This says that the creature must succeed on a check against the escape DC in the monster's stat block. That indicates that it's talking about a single escape DC, a single monster, and therefore, a single escape attempt.
So, this makes it clear how to deal with different creatures with different escape DCs - the grappled creature has to make a separate escape attempt for each one.
All the creatures you've listed have grapples that work exactly the same way, just with slightly different numbers. So, as above, the grappled creature would have to make a separate escape attempt against each escape DC.
This is a fairly powerful tactic at low levels, but against stronger creatures the initial grapples are unlikely to succeed, and higher level enemies often have ways of dealing with grapplers (like teleporting out, or just killing them all at once). It's also important to remember that you can't grapple a creature more than one size category larger than yourself, so your snakes will never be able to grapple a tarrasque (for example).
With all that said, if this tactic is becoming a problem, the DM might consider allowing a monster to burst out of multiple grapples at once, especially if it's clearly strong enough to do so.