Problem 1, the length of the pattern m is less than n.
There is a typo in problem 2 regarding the definition of the delta function (some variable "m" should be"i" instead). I've corrected the typo and uploaded the correct version.
Problem 3, You might be able to get bound better than O((m+n) log n).
Problem 4.
Q :Why can't we just
Delete(x);
Insert(k)
A: you need to implement delete(x). If you just remove the node, it is no longer a binomial tree.
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