Hi S-V,
(1) Manas is really just one among several words for the mind, and this is how it should normally be translated. But since we are here dealing with verse, we can expect that words will often be used quite loosely, and for this reason we need to be a bit more careful. The way mano is used in these two verses certainly seems to tie it to intention, and for this reason I think your translation “intentional mind” is reasonable.
With the word manasikāra, however, we are probably dealing with an ordinary usage of the word manas, and as such it should probably be translated as “mind.” The word therefore means something like “mind-action” or “work of the mind.” This of course implies intention, and it is from this that you get translations such as “attention.” In this case I think your suggestion “intention to act” is a bit too narrow.
For yoniso manasikāra it is the same. It means “wise work of the mind” in the broadest sense.
(2) All three can be generic references to the mind, but depending on the context all three words also have technical meanings. Just to give you some idea, viññāṇa in a technical sense refers to awareness devoid of the other aspects of mind. This is a purely technical usage, since in reality no such independent awareness actually exists. Citta in a technical sense can refer to samādhi. In this case the usage is technical because it limits the meaning of citta to a very specific set of mental experiences. Manas used technically refers to the experiences of the mind, when these are contrasted with sensory experiences.
So what I am saying is that context is all important. And if, in a particular context, there is no reason to believe that the term is used technically, then you can assume it the generic meaning of “mind” is intended.
(3) Paduṭṭhena is related to padosa, which is essentially the same as dosa. Dosa has two meanings in the Pali Canon. The most important one is “anger/ill will” (the usual translation “hatred” is really far too strong). But dosa also mean “corruption” (of mind) in a more general sense, and I suspect that is the meaning here. So any term that is roughly equivalent to “corrupt” or “defiled” should be appropriate. And yes, it is closely related to the three terms you are referring to.
(4) There is little difference, but they point to different functions and/or aspects of the defilements. Kilesa is a general term for defilement. (Which, by the way, is very rarely found in the Canonical texts. The semi-equivalent Canonical word is upakilesa, whereas kilesa is mostly found in the commentaries. The fact that so many Buddhists, monastic or lay, always use kilesa is just one among many indication of how thoroughly influenced we are by the commentaries.) Akusala-mūla highlights the fact that the defilements are the roots of unwholesome actions. Āsava is normally used for the most sticky of all the defilements, the roots from which all the other defilement ultimately derive.