I’m in Chicago and most of my team is in Paris, so this is a situation I have a lot of practice with!
My primary recommendation is: reference the time of your audience.
However, the key fact is: anything you say nicely is fine.
Typical conversations I’ve had at 8 AM my time (CST), 3 PM their time (CET):
Paris: Good morning!
Chicago: Good morning! uhh . . . Good afternoon!
Paris: Good morning!
Chicago: (Yes, it is a) good morning!
Paris: Good morning!
Chicago: Good afternoon (to you)!
These generic expressions of goodwill are fairly flexible. Primarily, we are wishing that people hearing us are enjoying whatever time of day it is. The same words can also acknowledge their wish for us, or even confirm that we are enjoying whichever time of day it is. That means whatever you say, you are justified, but generally it is more polite to acknowledge the reference frame of the people you are speaking to.
Remember, all this etiquette is rooted in practices that predate international conversation by a long shot. This is something that is acknowledged as awkward among native speakers and we laugh about it.
It sounds like your coworkers are treating this type of statement primarily as a report rather than a wish. They are saying “(it’s a) good morning (here in the US)!” This means you have two polite options! You can adopt their sense of the greeting and report from your own locale: “Good evening from here!” OR you can politely wish that they go on having a good morning in their location! Either’s fine, or even both!
Whatever you put in the Subject line of an email should contain a brief summary and be relevant to whatever is in the body.
In your examples
Regarding application for the post of product manager
Regarding scanned copy of my ID card
one would expect the Subject lines to be instead
Application for the post of product manager
Scanned copy of my ID card
The Subject line can be made even more specific by adding *your name followed by a '-'(hyphen) and the rest of your planned Subject line
John Doe - Application for the post of product manager
Jane Doe - Scanned copy of my ID card
int his way it is easier for the recipient to search for you without needing to remember you remain address.
Most email programs will prepend RE: meaning in regards to or in response to when replying to an email. The response Subject line would then look like this
RE: Application for the post of product manager
RE: Scanned copy of my ID card
Using regarding in your example is not necessary since the email is obviously regarding whatever is also mentioned in the Subject line. It is usually better to be less wordy as with a headline
Best Answer
E-mail subject lines are generally short fragments. I would avoid using a full sentence ("May I come to you office to discuss the possibility of joining your lab?") or placing the key point of the e-mail in the subject ("Question about joining your lab").
The actual subject line is up to you but I would consider something like:
And then explain one's intentions in the body of the e-mail.