It's not good to redefine the letter T (it was an alphabet, now it is a string).

I am not sure you give sufficient details. The important fact is not that there are 11 digits but that they form 10 pairs of consecutive digits (first + second, second + third, ..., 10th + 11th). The rest is correct.

This string contains "01" twice.b)0011220102.

Find the number of triples that can be formed from the given alphabet; let's call it n. A string of N digits must contain at least n + 1 triples. So, n + 1 consecutive digits serve as the first digit of a triple, plus you need to add two digits to form the last triple.c)I don't know.How should I proceed?

By the way, such sequences are called De Bruijn sequences. In that article, a string with no repeated pairs in alphabet {0, 1, 2} is denoted B(3, 2). De Bruijn sequences are cyclic; to get a regular sequence this problem is talking about one has to take B(k, n) and add the first n - 1 characters to the end.