Liquidity amounts calculation and AMM behavior in lower and upper boundaries points

[OoXooOx]

1. Let assume that I want create new pool with assets:
   token0: 5000
   token1: 20000
   In this case:
   Price current - 4
   And I provide liquidity in range:
   Price lower - 2
   Price upper - 7
   I calculate liquidity by formulas and choose lower value from them.

Next I must recalculate amounts which I must put in pool in real, because due rounding I must do this
and I receive amount0 4166 amount1 19999
So from my wallet will be subtracted only this amounts right? What happened with surplus?
They return to my wallet? Or this amounts must be calculated properly before transaction?

2. Next question. We have pool with params from above. So when price go to 2 all liquidity position will contain only token0.
   And here (Questions about liquidity calculation #60) you said that we do not have liquidity in
   boundaries and price must go to next price range. And its logical, because if we have AMM formula xy=k on lower border point
   y will be 0 and we receive p=0 and k=0. It's nonsense. Ok. But.
   Next sight of this situation - price go to lower point - 2. And now I can use this position only for buying token0, but I can do it.
   I have all position with toke0 and lower price - 2. So if I put in pool token1, then I receive some of token0. Right?

So question is how this happened. From first sight we can't use xy=k in boundaries. But from other side - we can use pool.

[OoXooOx]

1. Amounts recalculate in Pool SC in mint, modifyPosition functions and then via callback we just take right amounts from user.
2. https://youtu.be/oGOunGKMA-M?feature=shared