What is this saying about the relationship between Kamma and Dana?

MN 142 The Analysis of Religious Donations explains in detail the interaction between karma and dana (donations). In short, the result (kamma) depends on the mental purity of the giver and the recipient. And giving to the sangha (community of monks) is more meritorious than giving to any individual, even the Buddha.

Let's try to explain this:

This allows for ... the subjective escape from kamma through the alteration of one's mental state.

Alteration of one's mental state can be accomplished by ... a change in attitude or orientation or point of view concerning that which constitutes the self.

Firstly, charity can remove the stain of selfishness from the mind. That's a "change in attitude concerning that which constitutes the self".

This was said by the Blessed One, said by the Arahant, so I have heard: "If beings knew, as I know, the results of giving & sharing, they would not eat without having given, nor would the stain of selfishness overcome their minds. Even if it were their last bite, their last mouthful, they would not eat without having shared, if there were someone to receive their gift.
Iti 26

AN 8.33 states 8 reasons for giving. However, AN 7.52 (below) states that adorning the mind is the highest reason for giving. From this answer, "adorning the mind" means making the mind more virtuous.

“Sāriputta, someone who gives gifts, not for any other reason, but thinking, ‘This is an adornment and requisite for the mind’, when their body breaks up, after death, is reborn among the gods of Brahmā’s Host. When that deed, success, fame, and sovereignty is spent they are a non-returner; they do not return to this state of existence.
AN 7.52

And what's the purpose of virtue? That's answered in AN 10.1. Virtue ultimately leads to mental purification and liberation.

Virtue leads to a "change in orientation or point of view concerning that which constitutes the self".

the understanding i get is letting the deed (action) takes care of itself. the giver is only focused on the intent with the right feeling behind the intent. once that is well-formulated the giver does not worry about the resulting process, ie., the intent becomes the driver of the process. by getting attached to the process the purity of the deed is lost. this answers parts 1,2 and is corroborated by the following passage;

One gives without attachment because the most powerful single factor in the making of a deed of magic (and giving to attain an outcome of any sort is conjuring, or magic) is Letting Go. You need to release the wish. Let the intent find it's own way to work itself out. If you try to control the outcome you are assuming a role beyond your scope.

part 3 of your question maybe refers to know-how. it seems to imply that although one isn't attached to the resulting process, skillfulness (past experience) will surely produce a better outcome. the passage says:

One can understand this in a very ordinary way: given a complex task and two individuals to perform it, which would you expect to complete the task successfully: the muddle-head or the clear thinker?

so if the task at hand requires training, skill, etc., well-wishing and detachment alone are not going to produce good results. i guess maybe that's what part 3 of your question is saying.

still another way to understand part 3 of your question, when the intent is a good one, but the consequences are perceived as bad. for example, a recent story where the intent to save livestock from disease is a good one, but the actions taken to do so - killing wildlife - are perhaps not nice. here, the experience of the consequences needs to be felt in order to understand how intent can manifest itself. they say, "the road to hell is paved with good intentions"

after thinking over, some of the reading hints of the giving/receiving process as donation in return for blessing, and in which case as stated, "the giver was the primary beneficiary of the act of giving," in this case, the "receiver" is not doing anything mechanical in nature; it's all intention-based. this is maybe where the adage, "a blessing in disguise" comes from. or maybe the saying insinuates a blessing desired by the "giver" has less power than if they were detached from the result. oh well...