Why does Gai look like Rock Lee? Why does Gai-sensei and Rock Lee look almost exactly the same? Are they from the same clan or are they blood-related? Hinata and Neiji look the same and they're cousins, same with Sasori and Gaara, Sasuke and Itachi, so they're probably blood-related, or they're not? Are there any explanation regarding this?
No, they are not blood-related. When Lee wasn't in Guy-sensei's team yet, he was often mocked and bullied because of his inability to use any techniques other than Taijutsu. Guy-sensei was the first one to really believe in Lee's abilities, and thus he became Lee's idol. From the wiki:


  When first joining Team Guy Lee's appearance changed drastically. He had shorter hair than before that curved upwards in the back. He still maintained the Chinese appearance, since he wore a robe and a martial arts belt around his waist. After joining Might Guy's team, his appearance changed considerably to emulate his idol and sensei. 


Here's an image of how Lee used to look:



So, as you can see, he just changed his appearance to look more like Guy whom he idolizes.