Why $\rm He^{++}$ is more opaque than $\rm He^{+}$ and so absorbs more energy? In the Cepheids, $\rm He^{++}$ is more opaque than $\rm He^{+}$ so it absorbs more energy.
If it is because a more charged particle have a higher electromagnetic field and the stronger the field, the more the photon will interact with it. How can we explain that formally (perhaps with Feynman diagram if required)?
 A: I dispute your claim. Doubly ionised He is comparatively transparent. The mechanism that excites Cepheid pulsations is the high opacity of partially ionised He. 
Normally the opacity increases with density and decreases with temperature in stellar interiors. The dependence on temperature dominates and thus when a layer is compressed, the opacity decreases and allows heat to escape. In a partially ionised He layer this does not happen. On compression, such a layer becomes more opaque due to increasing density and because of photoionisation which allows the compression to occur without a big rise in temperature. Or in other words, the opacity increases as the temperature increases. This traps heat by ionising the He. The heat is then released as the layer expands and cools. Once He is mostly doubly ionised, then this mechanism no longer works.
I guess you are getting your information from Wikipedia. I'm afraid it is wrong on this. Try these lecture notes by the colossus of stellar radiation hydrodynamics - Mihalas. The relevant bit is the first paragraph of section 3.
