Supplications

One can make general invocation and thikr to Allah as well as general Du’ah.

It is an issue of dispute among scholars. I prefer the opinion that says that it is after Maghrib.

Morning is after fajr but evening is an issue of dispute. Some scholars say after Asr and others say after Maghrib. I take this last opinion.

Yes.

Yes, you can.

I know that whoever recites this supplication, Allah will relieve him from his depression and calamity. I don’t know about the 3 times as I don’t believe that it is part of the Sunnah.

You can make general Du’ah as there isn’t anything specific

There is a hadeeth that recommended making Du’ah while raining.

This is true. It is sufficient to say Subhana Allah. It is best to say: Subhana Allahi wa bi hamdihi, Subhana Allahi Al Atheem.

To say it in a specific number is not part of the Sunnah. You may offer your salutation as many as you want but without restricting it to a number. The best on is the longest on which is known as al salawatul Ibraheemiyah