If you look the chain of events that lead to one another in the Dependent Origination, you may conclude that just after 'contact' (the encounter between the senses, sense stimuli, and consciousness) we can experience by ourselves the mentioned processes in action.
Feelings are the result of contact, and there are three general kinds (applied to each of the six senses): pleasant, unpleasant and not-pleasant-nor-unpleasant.
When ignorance fetters the mind, we don't understand that pleasant feelings are not so much a quality of the objects, but a modality and process of the mind dependent on the object. We think that only the desirable objects can give us pleasure and well-being, and so, we like those kinds of object which use to give rise to pleasant feelings. The ignorant mind doesn't see feelings as feelings, but sees the object as desirable and a source of pleasure to be acquired.
But sometimes we see for ourselves that pleasure is not always present when the objects considered desirable are present as well: Have you eaten so much of something you like that you get to a point where the mere thought of that food makes you want to puke? Why did the object suddenly lost its "pleasant status"?
We say "we like X thing" when we attach ourselves to the pleasant feeling X make us feel. And the more X give rise to that feeling, the more we confirm to ourselve that we like that X thing. The idea of liking gets even more consolidated (and feels more real and tangible) especially when we define ourselves as "the one who likes that X thing". Think in how many people define themselves as "gamers", or "movie geeks", or "drug addicts", "believers", or "christians"... Their identity (the idea of what their "self" is) gets defined by their likes and dislikes, which are defined by our attachment to past feelings.
EDIT: I didn't read the last part of the question.
To know why the same object feels different for two persons, I think it would be useful to ask to ourselves if we feel the same feelings over time. Do the things you liked and disliked during your childhood keep the same to the present day? Do you like and dislike the same things, now and then? If not, what makes the those feelings change over time?
Feelings and perception of what is being felt go conjoined. If perception is altered, so is feeling.
Perception is the faculty that allows us to know what an object/phenomenon is and what qualities belong to such object/phenomenon.
Views are our internalized ideas and assumptions about our experience of reality, about how reality is constitued, about how the components of reality interact with each other, and how we fit in all of that conceptual framework. Most of times, we are not aware of our views, but they are the assumption which create expectations about consequences of our possible actions; views lead our behavior, whether we aware of them or not.
Perception can be altered if our views are modified; and views can be modified by thoughts. In time, reflection can be modified or "tuned" with precise data through personal investigation and reflection, or by some external source (a book, a teacher, our parents, our culture, our friends, etc.)
Most people have different views about the world and reality, and thus, their perception of sense data varies from one person to another, or from the "same person" in a moment X compared to a moment Y.
Also, and not less important, our senses are part of the form aggregate. If our senses are structuraly different, then it is possible that feelings may differ as well.