How to create new language with languages $L_a = \{a\}, L_b = \{b\}$ and set operations?
Part 1. is ok. The idea behind is that you have to take the letters 2 by 2 and then make the star closure. Call $L_e$ the language of even words you just defined.

Part 2. Assume for a moment to have defined $L_o$ the language of words of even length from $L_a$ and $L_b$. Then to have even length and different initial and final letter you can just define

$L=L_a\cdot L_o\cdot L_b\cup L_b\cdot L_o\cdot L_a$

Remark that words in $L$ have length at least 3 since $a$ starts and finish with the same letter...

To define $L_o$ the idea is that an even word is just to exploit $L_e$:

$L_o=L_a\cdot L_e\cup L_b\cdot L_e$.