Hi! Although you might not want to hear from someone with such a rating, well, give me a chance, I hope I do better in upcoming rounds :D
1) The 250-point problem: ( Link )
In this problem, the main thing to notice is that the sequence is either of the form "xo" or "ox" repeated n / 2 times. Thus, we can test the known letters and see which type they match, and print the one that matches.
2) The 500-point problem: ( Link )
Here, the most important note is that if x XOR y = z then y = x XOR z. So, we can try all pairs of a plaintext XOR a ciphertext to be key, then check if it's valid. A key is considered valid if, for every ciphertext, there exists a plaintext which when encrypted using the current key gives this same ciphertext.
3) The 1000-point problem: ( Link )
First, you need to read the statement carefully, as it clearly states that the characters in the original message are distinct, and thus the characters in each subsequence are distinct. Now, we can consider the given subsequences as "letter x is before y" relations and put those as edges in a graph. Note that if you're given a subsequence x_1, x₂, ..., x_n, then for each i, x_i comes before all x_j : i < j <= n. Now that we have the graph, all we have to do is a topological sort. Since we're being asked for the lexicographically minimum string, among the zero-in-degree nodes, we choose the one that corresponds to the lexicographically minimum character.
I hope the explanations were clear, if you notice anything wrong or vague, please tell me :D