Concerning the Open Hand Technique, if I have a level 6 Monk and I flurry of blows on a single target and I hit with all attacks, can I apply a Str save to all attacks to possibly push a mob back a total of 60 feet? Basically, does it go off once, or multiple times?
You can apply an effect to each hit you make on an enemy. The key phrasing here is:
Whenever you hit a creature with one of the attacks granted by your Flurry of Blows, you can impose one of the following effects on that target[...]
So whenever you land an attack, you can apply an effect. If you land multiple attacks, you can apply an effect on each hit. That said, there are a few problems with your idea. The first is that Flurry of Blows only grants two attacks:
Immediately after you take the Attack action on your turn, you can spend 1 ki point to make two unarmed strikes as a bonus action.
The second problem is that you don't make the attacks simultaneously. When you hit with the first attack, you roll damage and apply one of the effects. From page 194 of the PHB:
Whether you’re striking with a melee weapon, firing a weapon at range, or making an attack roll as part of a spell, an attack has a simple structure.
Choose a target. Pick a target within your attack’s range: a creature, an object, or a location.
Determine modifiers. The DM determines whether the target has cover and whether you have advantage or disadvantage against the target. In addition, spells, special abilities, and other effects can apply penalties or bonuses to your attack roll.
Resolve the attack. You make the attack roll. On a hit, you roll damage, unless the particular attack has rules that specify otherwise. Some attacks cause special effects in addition to or instead of damage. If there’s ever any question whether something you’re doing counts as an attack, the rule is simple: if you’re making an attack roll, you’re making an attack.
Each attack resolves separately, including the special effects you add to it. So you can't hit the enemy twice to push them back 30 feet.
What you can do is push the enemy back 15 feet, then run up to them and then hit them again, and push them back another 15 feet. The exact rule for moving between attacks is (PHB, page 190):
Moving between Attacks
If you take an action that includes more than one weapon attack, you can break up your movement even further by moving between those attacks. For example, a fighter who can make two attacks with the Extra Attack feature and who has a speed of 25 feet could move 10 feet, make an attack, move 15 feet, and then attack again.
One per hit (maximum of 2)
The Player's Handbook clearly states:
Whenever you hit a creature with one of the attacks granted by your Flurry of Blows, you can impose one of the following effects on that target:
Emphasis mine. Let's talk about the first emphasis:
One of the attacks - this means that if an attack hits, you can then impose the second emphasis, which is;
One of the following effects - then you can choose which one effect to impose on the target.
Since Flurry of Blows spends 1 ki point and your bonus action, you can only Flurry once on your turn. Since you can only have one bonus action on your turn (PHB page 189):
You can take only one bonus action on your turn, so you must choose which bonus action to use when you have more than one available.