According to Mahayana (Yogacara) Abhidharma,
cetana is connected with traces and dispositions (samskara) left by previous actions and experiences. (What follows is my understanding based on my study and practice. Not official but I did spend some time contemplating this stuff, and I think I've got some insights) Like you said, cetana can be
akusala (healthy or unhealthy). It is like having healthy habits or unhealthy habits. Our habits define our directionality of mind and our tendency to act or react. The concept of cetana is part of the model in which everything happens by itself, there is no person who intends - instead, if your habit is e.g. to indulge in negative thoughts, your attention will keep getting drawn to imperfections - even if there are many other potential objects. Cetana is impersonal and automatic.
Sankappa (samkalpa) or aspiration is part of a different model. It is what you want, you're trying to achieve with your behavior, what you're going after. So samkalpa is a lot more personal, it is not happening by itself, it is what you are driving at. Now, sometimes (actually a lot of time for the untrained people), we don't actually act with a clear purpose in mind. Oftentimes we simply let our traces and dispositions drive us. We act out our opinions, preferences, aversions, desires etc. without thinking of consequences that much, and not even having a clear goal of what we're trying to achieve. So what Buddha meant with his "samyak-samkalpa" (I'm using Sanskrit spelling here) is acting with a constructive purpose in mind, trying to make things better - not just puking out our predispositions.
By now you should have an idea that cetana and samkalpa are kinda different in one sense and kinda two sides of the same thing in another sense. In one sense, cetana is how your tend to act "unconsciously", whether you're paying attention or not - whereas samkalpa is what you think are trying to achieve "consciously". In the second sense, samkalpa is really just a manifestation of cetana at a higher organizational level. In yet another sense, both are manifestations of samskara (imprints, traces).
All models have limits though - this becomes apparent when you try to connect these two models (impersonal and personal) together: can we say that healthy predispositions always manifest as wholesome aspirations and vice versa? Not so much!
One example is when we force ourselves to act against our (bad) habits. Should we say that in this case our cetana is unhealthy but our samkalpa is wholesome? Or should we say that in fact some positive change of cetana has already happened, although at this point it is only a partial/superficial change? Another example, is when we have wholesome aspiration (e.g. to attain Nirvana) out of an unhealthy cetana (e.g. aversion of the world). Should we consider an unhealthy cetana as healthy when it drives a wholesome aspiration?
From Mahayana perspective, this is an example of Emptiness kicking in - this makes it clear that cetana and samkalpa are not truly existent entities that are strictly in one state at a time. They are merely simplified designations for a large number of samskaras responding to various stimuli. Things only look concrete when you look at them from the distance. Once you step in closer, they split into multiple components that work by their own rules.
So does it mean cetana and samkalpa could be kusala or akusala independently of one another and there is nothing useful we can learn about them? Luckily, that is not so bad. The general rule we can extract from this, is that our mind exhibits the quality of inertia: Having an aspiration for something does not automatically mean we have changed deep inside. Sometimes we may ourselves not realize the hidden agenda behind our action, which can come from unhealthy predispositions and be in fact unwholesome, egoistic etc. We have to apply right view, right effort etc. over a long time in order to overcome the inertia and have dharma become our second nature. As one of my teachers explained, the transformation is complete when our acts are spontaneously wholesome without any effort needed from our side.
For a teacher on the path, this inertia can be used as upaya - motivating the student by taking advantage of their illusions/attachments/aversions. For a student on the path, this inertia can manifest as a form of hypocrisy - when the student is superficially a Buddhist but in essence is still full of grasping, negativity, conceit, us/them thinking etc.
To get to your examples:
If your purpose (samkalpa, aspiration) is to accumulate (material things, a state of becoming): is it possible to maintain wholesome intentions (cetana, habitual tendencies)?
Yes. The purpose/aspiration "to accumulate" is not necessarily unwholesome. It could be wholesome (kusala) at mundane level but not conducive to liberation (sasava, not anasava). A householder aspiring to accumulate wealth to provide for well-being of the family and community is a wholesome aspiration, just not a liberating one. So one can totally be a good householder aspiring to accumulate things while maintaining healthy cetana.
Now, if you are asking if one's aspiration "to accumulate" could be a compatible with the Path (anasava) - the answer is, provisionally yes and ultimately no. On the initial stages, the task of the practitioner is exactly "to accumulate". To accumulate what? Merit (good karma) and knowledge (of the basic teaching). This is why such stage is called The Path Of Accumulation. However if one gets stuck on this stage for too long, it can turn into Spiritual Materialism, when we accumulate goodness and knowledge as a way to feed our ego - instead of deconstructing it.
Buddha recommended the right aspiration (samyak-samkalpa) to be the aspiration towards progressive improvement, which on initial stages is identical with accumulation of mundane wholesome qualities but on the advanced stages becomes distinct as we get to stalking our ego/attachments, practice non-abiding (baselessness) etc.
For example: you like to have a monastery be built, you like to have a medi-community to grow, to be maintained.
Dreaming about monastery sounds like a typical case of spiritual materialism. Instead, someone should focus on non-abiding (baselessness) - which includes letting go of the raft. Once the first bhumi has been achieved, and there is no longer aspiration to attain Nirvana, one can build monastery etc. and it won't longer be an obstacle.
If your intention (cetana, habitual tendency) is wholesome, is it possible to strive after a non beneficial purpose (samkalpa, aspiration)?
Yes. There are two cases here. One is like I said, you could be mistaken about your intentions (predispositions). You could think you're a Buddhist while in fact being a regular sloppy person who just happens to know a lot about Buddhism or a regular grumpy person etc. Second case, your predispositions could be healthy but because of the change in your environment you could be forced to act with unwholesome aspiration in mind. This depends on the supporting condition of ignorance. An example of this is a well-brought up child of a good family who gets into a bad company. The natural instincts (cetana) of such child are still good but the environment provides negative motivation, which effects the wrong view, which drives unwholesome aspiration.
If your intention (cetana, habitual tendency) is unwholesome, is it possible to strive after a beneficial purpose (samkalpa, aspiration)?
Yes, like I said, because of the inertia you may have habitual tendencies (cetana) that go contrary to your aspirations. You can have unhealthy predispositions (cetana) while aspiring towards a more healthy vision.
If your purpose (samkalpa, aspiration) is to let go (of material things, states of becoming): is it possible to maintain unwholesome intentions (cetana, habitual tendencies)? For example, you have building material and you are willing to let go of it, you have time and you are willing to let go of it.
It's not like our goal is to let go of everything for the sake of letting go. Then the poorest person would be the Buddha - this sounds like the extreme path of renunciation, not the Middle Path. In Buddhism our goal is Unbinding, which is about not getting stuck - not about avoidance/isolation.