Hello Shan Gao,
that you have focused on motion in order to address the question of time is a novel but very fitting approach. it is indeed the perception of relative motion which gives us a sense of time.
i'm not an expert in physics, but, when i read:
3. Understanding RDM in terms of instants, for example, how a particle "knows" which position it will be at next instant in the sense of probability.
my first thought was "Feynman". he's fairly much the master on probability and motion.
a quick search of the web turned up:
Feynman's path integrals and Bohm's particle paths
and Feynman's path integral formalism have something to do with particle .... provided a probability distribution on the space of all paths, ...
www.iop.org/EJ/article/0143-0807/26/3/L01/ejp5_3_l01.pdf - Similar pages
by R Tumulka - 2005 - Related articles - All 6 versions
downloading the pdf, i found:
"This theory would have the same ontology as Bohmian mechanics, but a different, in fact stochastic, law of motion."
he also has time as discrete. Tumulka appears to be looking at very similar things as you are. what he has to say in the paper may be helpful to you. his writing appears to be about as clear as your own.
you might also find 'time counts', another entry here, of interest, though maybe not as specifically relevant.
matt kolasinski