It seems that there is no common solution for such case — it depends on tasks and goals. I had a case for dashboard displaying warranty & repair information about equipment. I made such assumptions (maybe inappropriate to common cases):
1) Making roundings for timestamps and dates are incoorect, because it is not possible to make difference between correct and rounded values — the user may be confused. Only relative values ("1 hour 23 minutes 35 seconds ago") should be rounded.
2) The nearer the date/time to present date/time, the more accurately it should be displayed. For instance, if it is two days to start an review/repair activity — it should be displayed as 2 days (with an exact date and time). But if the equipment should be checked at 2015.12.28, it is enough to say "more than 3 years, at "december 2015", or event "at 2015".
3) More human and task-oriented, and less mathematical roundings are better. For instance, "1h29m ago" can be rounded to "more than one hour ago" for alert messages and to "less than two hours ago" for news feed (but the usage of such text format instead of numbers should be additionally checked for readability — for instance, it is usually not applicable in lists or tables).
4) Combining both exact date and time and, visually separately, rounded relative value is more effective in date/time critical applications (for instance planners and this dashboard).
So, with such assumptions, answers to your questions:
1) Yes, roundings are applicable for relative values, because they are easier to understand (no necessity to compare with current time).
2) Using day names instead of realtive values can be harder to understand, cause it also requires additional cognitive efforts.
3) Yes, relative values for days and months can be useful in some date/time crytical scenarios, but in case of simple informative messages (as in news feeds) it is unnecessarily.
4) Time can be dropped if it is not vital and if the moment was more than two days ago (or will be after two days).