The concept is fine
... the details are a little off.
Surprise affects creatures, not rounds
The DM determines who might be surprised. If neither side tries to be stealthy, they automatically notice each other. Otherwise, the DM compares the Dexterity (Stealth) checks of anyone hiding with the passive Wisdom (Perception) score of each creature on the opposing side. Any character or monster that doesn't notice a threat is surprised at the start of the encounter.
So, you are hiding in the Rope Trick - this is no different from hiding in the wardrobe or, for that matter, in the shadows. Your party makes a group Dexterity (Stealth) check. Because a Rope Trick is a very good place to hide, your DM may allow you to make this check with advantage (I would). This ability check sets the DC that the opposition will need to overcome with the passive Wisdom (Perception) to avoid surprise.
But, I hear you ask, if I can't be seen, how could the perceive me? Well, you are a adventurer in a fantasy medieval role-playing game so you haven't had a bath in 2 months so basically - you stink. The Rope Trick hides you from view and stops attacks but it doesn't stop your stench. Similarly, your fighter friend shakes nervously whenever he's waiting for action so if you can hear his chain-mail jiggling so can the guys you want to ambush. All of this random stuff is what the ability check represents.
Now, if the people who you want to ambush rely predominately on sight to perceive things (most creatures do) they will have disadvantage on their Perception checks. So assuming at least half of you roll somewhat decently you have a good chance to surprise most creatures.
Falling is instantaneous and if you don't take damage, you remain standing. If you fall from less than 10 feet you don't take damage so that all works.
There are no rules for a "death from above" type of attack. A kind DM may give you advantage on your first attack - I'm not that kind.
After surprise is determined and before anyone does anything initiative is rolled. The mechanics of surprise have been dealt with at length in numerous questions.
Attacking and Movement
Attacking and movement are "simultaneous" in that you can do both on your turn. Mechanically, movement can be interrupted by attacks (or spellcasting, hiding etc.) so you can move, fall, attack, move, attack, move etc. which are each resolved sequentially but are narrativly a series of fluid interconnected motions. Its analogous to the fact that dancing is more than following the dance steps - D&D uses the steps to resolve the action but in "reality" its all a seamless whole.
Is more about how you interpret and narrate the results of the dice and less about what the dice actually say. The dice can tell you you hit for 12 points of damage and sometimes that's what you will say and that is perfectly fine. However, its more cool to see the result and say - "With a primal yell, Thugnar steps out of the Rope Trick and plunges on the unsuspecting rabbit. Before it has time to let out a squeak of terror, his greatsword enters its back and tears through fur and flesh with a spray of blood. It takes 12 points of damage. Is it dead?"