Does a major revision mean my paper is likely to be accepted? How do I answer comments that would change the paper a lot or conflict with my design?

In my experience, if I am given a major revision, more than 95% of the time the paper is accepted. The remaining 5% that are rejected usually meet a reviewer who takes an oddly superior stance and does not consider the authors' position, or were submitted to a journal with a very high impact factor, whose acceptance rate is low enough that it can afford to behave this way, and no one dares complain.

When a sincere response is still rejected, it is usually because you did not understand what the reviewer really wanted. If the points the reviewer truly cares about are not addressed, the reviewer may become frustrated while reading your reply and simply reject the paper.

Reviewers who give detailed comments raise many points, but there are usually two or three they consider fundamental, which you must answer effectively or even change the paper for. The reviewer may already have in mind, "If you answer this way, I will let it through."

But if the authors do not understand this, or keep insisting on their own position, it usually ends badly.

If you think a reviewer's comment is too vague, or so abstract it is almost philosophical, it is actually easier to answer. The reviewer asks in general terms, and you can answer concretely, choose suitable ground, and attach enough references and even figures. Even if the reviewer remains unsatisfied, when the editor looks over the exchange, there is a good chance the editor will see your good faith and conclude that the reviewer is being difficult.