I think my answer here should give you a pretty clear idea of what Burnt Norton is about.
Although some minor details (for that matter analytical tools as well) might be open to interpretation, the major motifs and themes are pretty well known and well discussed. It is about Christianity, clearly, unambiguously. Even in Eliot's time, a lot of commentaries and criticisms focused on the religiosity of the poem.
George Orwell comments on the poem:
So long as man regards himself as an individual, his attitude towards death must be one of simple resentment. And however unsatisfactory this may be, if it is intensely felt it is more likely to produce good literature than a religious faith which is not really felt at all, but merely accepted against the emotional grain... Eliot's escape from individualism was into the Church, the Anglican Church as it happened. (All Art Is Propaganda: Critical Essays)
Let's look at your cited lines
And time future contained in time past.
The reason the future is contained in the past is that the choice has been made and our path has been chosen for us. He is talking about the one most critical moment in human history, according to Christian cosmology: the fall of man. Of course you could interpret this part also as a mediation on our mundane life. Sure that is not a problem. But it should be noted the poem was written right after Eliot converted to Anglicanism and at a time when he was waxing religious.
Both the past and the present may be present in the future because the present is viewed by Eliot as a fixed point onto which both the past and the future fold. Also later in the poem he goes
Time past and time future
Allow but a little consciousness.
To be conscious is not to be in time
But only in time can the moment in the rose-garden,
The moment in the arbour where the rain beat,
The moment in the draughty church at smokefall
Be remembered; involved with past and future.
Only through time time is conquered.
Time is continuous, and the past and the future cannot be separated from the present. To be conscious does not give us enough to be in time, because by being in time, immersed in time, we need to be aware of the past and the future. And only by achieving that can we call to mind, understand, and appreciate the moment we had in the Garden of Eden, a moment
"in the arbour where the rain beat", and a "moment in the draughty church at smokefall". A total recall, if you will. Thus "Only through time time is conquered".