These are questions that should really be directed towards Flickr as only Flickr will know the answers for sure.
Should I wait after date change or that should be in effect right away after I chage the date?
I suspect it may take some time for any changes you make to propagate throughout Flickr's servers. I do not know how long it may take but new tags can take up to "a few days" before they appear in API searches according to this Flickr FAQ:
it shouldn't take more than a few days until your photos appear in searches, groups, etc.
How does it supposed to work if pictures are taken at the same day? TIme is counted in this case?
I would certainly expect the time to be taken into account, being that Flick have a time field that you can change.
If you have several images that have exactly the same posted date and time, then my best guess would be that they would be displayed in the order in which the uploads to Flickr completed (although I may be wrong about this).
You might want to post these queries in the Flickr help forum for definitive answers.