Two Ladder questions.

Are all these questions open? I don't know the answers to either of them. The first one is "can black force a ladder to go down?", and the second is "can white force it to go up"? Here are more precise questions.

1) Is it currently not yet proved that even on a 10000x10000 board, black cannot connect a second-row ladder to the edge? In other words, even if this board was huge,

can we *prove* that black has lost? The idea is that black might ladder along for a while and then play a random stone on the 6th row and somehow connect. In other words I am asking "is there a 2nd row ladder escape template with no stones in it?" Note that in another thread there was an example of a template with no stones which could connect black to the edge if black had both a second row and a 4th row ladder -- Tom's move is the trick.

2) A second row ladder can be moved up to the third row (by black), but white can't change anything alone -- if black decides to ladder on the second row white must continually defend on the first row.

White can however force a third row ladder to drop to the second row (although black can then move it back up again if they want).

In general, white can let any ladder drop down one or more row.

But can white ever force a ladder to go up one row? The play would be for white not to play directly under black's ladder but way below it, and then later on obstructing the ladder head-on when black can't break through, and hence forcing it up.

I should say that shalev raised the first question on the other thread about infinite hex.

With regard to question 1. , it seems intuitively obvious that any single ladder can not escape without some help no matter what the board size, but I do not think this conjecture have been proven.

With regard to 2), it is interesting to note that from 3rd row or higher white may drop to a lower level and in general  this is a weaker position for white (this is intuitive as black is closer to his edge)  however there are certain board positions where white can only prevent as escape only by dropping to the lower level.