As to Dogen's conception of Being-Time. I can give that to you in a nutshell. ... Here is my quick version. It helps to realize that Dogen was always proposing Reality from several perspectives at once, some seemingly contradictory (X exists, X does not exist), but just different vantage points, each true in its way:
So, we usually think that time flows past to present to future, and that events over 'here' and 'now' are not events over 'there' and 'then'. Well, that is true in its way. But Dogen also pointed out that the past is just a memory of the mind (it was, after all, just the 'present' back then), and the future is just a dream of the mind (what future has there been yet?). In that way, 'past' and 'future' are just dreams. So, without there truly being a 'past' or 'future', what need have we even for the word 'present' (which only exists as a concept in contrast to what is -not- the present)? If we compare it a little to a 'river', it is a little like saying that there is no 'upstream' or 'downstream' or 'here' to the river, if we just see it all as a single 'just-the-river'.
And because every place on the river is 'just the river', every drop of the river is 'just the river', everything happens SIMULTANEOUSLY! Both the top and bottom of the river are present simultaneously and are one. Because everything that is of the river is just the river, everything that happens 'here' happens 'here' 'there' and 'everywhere' too. (I don't like overly connecting modern physics to Dogen, but there are parallels: For example, we think of the 'Big Bang' as something that happened in the past, but in some mathematical models, it is happening right now and every time too. Furthermore, where in the universe is the 'Big Bang' not happening(?), because all came out of the Big Bang at once).
Further, there is a past and future too (there is, and there is not). But the future flows into the present which flows into the past. It is a little like saying that, though a river flows from upstream to downstream, you cannot have downstream without upstream. Downstream also flows into the upstream. Modern physics has come intrigingly close to this by saying that all timelines actually can be seen as running in two directions (the dominoes falling down can also be seen as the dominos 'unfalling up').
And every drop of the river flows into every other drop of the river, so that what happens to Drop X is the time and being of Drop Y. If you drink a cup of coffee, it is the whole universe drinking a cup of coffee. And if you are doing it here and now, the whole universe is here and now.
Furthermore, everything in the universe had its own 'time'. (Again, by coincidence perhaps, EInstein stumbled upon a model something like this a few centuries later). My clock is not your clock.
We also think of time as 'long' or short' ... but would a creature that lives its lifetime in a day or a creature with a lifetime of 10,000 years view time the same way as mankind? Are not 'long and short' subjective judgments of men, and is not 'time' just" time' (just what it is, not long or short)? And can we not say too that every moment is an eternity unto itself? .
And, of course, time is not separate from being, and being is not separate from time ... In other words, all of the above is just YOU!
And on and on it goes. It is just another way of seeing life and being as of one piece with all of space and time, with all Reality. It is just another way too of tossing a monkey wrench in our normal way of seeing events and who we are.
Now, I am out of time ... so time to stop.