Regular expression for containing 010 as a subword
In the first one, L1 = (a+b)*(aa+bb)(a+b)* not (a+b)(aa+bb)(a+b)* because in the second one, it is possible only to have one character of a or b and then we have to find the occurrence we need. Your L1 denies any word that does start with (aa+bb). It also forces all the words to start with a or b.

By the way, I use + for | and ∪.

So for the second one, it is in the same manner:

L1 = (0+1)*(010)(0+1)*

010 might occurs in the beginning, the middle or the end of the word.