which asymptotic are you interesting about? For instance, one can use Meet-in-the-middle for second problem...

First thought: you can treat numbers like binary vectors and construct a matrix, where each row is a binary vector, corresponding to a particular number in sequence. Then you can perfrom Gaussian elimination modulo 2 on this matrix and if you have at least one all-zeroes row you can get xor == 0. If for each row R you also save indexes of rows interacted with row R during Gaussian elimination you can restore the corresponding subsequence.

http://codeforces.me/blog/entry/1201
http://apps.topcoder.com/forums/;jsessionid=27C509BC366B5418E52684946CBFC0DF?module=Thread&threadID=704255&start=0&mc=5#1393888