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2) Rule to define this timestamp based on a another timestamp e.g timetampB=TimestamA, defines the time dropdown with both date and time information.

Issue 1:
When you define the DATE part on Timestamp1 the RULE executes to define Timestamp2, it defines the date field correctly but the time field is defined with both date & time.
Issue 2:
The whole Timestamp is considered DEFINED when only the date part is selected (defined) with Time field remaining undefined; meaning the RULE (to define Timestamp 2) will execute as soon as the date is selected (defined).
What happens now:
As soon as the date part of Timestamp1 is defined the rule (TIME_ADD) is executed and assumes Timestamp1's time filed is 00:00 AM, and it defined Timestamp 2 as 02:00 AM. I want to for example, set the time as 07:00 AM and once I define that, the RULE will execute and define Timestamp2 as 09:00am.
Solution:
Rule to fire only when both date & time fields are defined. That way when I define the time field the TIME_ADD rule will define the correct Timestamp2 time field and not 02:00 am.
Reason:
When both date+time is defined then the FUNCTION TIME_ADD will work properly.
Example, a RULE to define a Timestamp2 two hours more than the first as in order requested between Timestamp1 and Timestamp2, the rule will change the second attribute to allow 2 hours between the 2 e.g Order between 7 AM and 9 AM, not 7AM and 2 AM.
Issue 3:
System always assigns 00:00 to the time field, even when not defined. I know this is intentional.
If you have set up a time range and 00:00 does not fall in this range, the system will still assign it as 00:00 and potentially cause problems.