Is there an explanation for Natsu's motion sickness?
Not only Natsu, but every wizard having Dragon Slayer Magic is prone to motion sickness. During the Grand Magic Tournament, all four Dragon Slayers suffered from motion sickness, i.e. Natsu, Gajeel, Rouge, and Sting. It is also confirmed in the anime that, Laxus suffers from motion sickness as well. The only exception is Wendy, but considering that she has Magic to counter motion sickness, it might not be affecting her.

It has not been explained, but it is likely due to a side effect of the Dragon Slayer Magic.

Wendy's Magic does not affect Natsu because he built up immunity. This was specifically stated by Wendy herself.

Also, Happy doesn't affect Natsu because Natsu doesn't consider Happy as a vehicle. This was also specifically mentioned by Natsu.

Edit as per the latest chapter: The motion sickness is caused due to inability of dragon slayer magic holder to adjust with the dragon's enhanced visual acuity which affects their semicircular canals.