[RPG] Can you kill a Tarrasque with the Open Hand monk’s Quivering Palm feature

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.

1. Choose a target. Pick a target within your attack’s range: a creature, an object, or a location.

2. 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.

3. 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.

The easiest way to gain advantage on a death saving throw is to use inspiration.

If you have inspiration, you can expend it when you make an attack roll, saving throw, or ability check. Spending your inspiration gives you advantage on that roll.

Alternatively, you could be a Wild Magic Sorcerer, and use Tides of Chaos. Well, probably.

Starting at 1st level, you can manipulate the forces of chance and chaos to gain advantage on one attack roll, ability check, or saving throw.

The 3rd- level spell Beacon of Hope explicitly grants advantage on death saving throws for its duration.

Fighters can use Indomitable to reroll a failed saving throw - not precisely the same as advantage, but pretty close.

Beginning at 9th level, you can reroll a saving throw that you fail.

There are almost certainly more options that I've missed - getting advantage on things is a pretty fundamental part of 5e.