The instant/moment/as soon as

Hi,

The fact that 'the instant/the moment' are used in the same way as 'as soon as' confuses me. Are they used as conjunctions?

For example:

As soon as I get the information, I’ll tell you.
The moment I get the information, I'll tell you.
The instant I get the information, I'll tell you.

Is it idiomatic to use perfect tenses after 'the moment/the instant' when they have the same meaning as 'as soon as'?

To talk about the future:

I'll go to the shops the moment/ instant it has stopped raining/I'll go to the shops the moment/ instant it stops raining

To talk about the past:

They restarted the tennis match the moment/ instant the rain had stopped/They restarted the tennis match the moment/ instant the rain stopped.

Also, I have a hunch that it would be incorrect to use 'the instant/moment' before 'I can' .

I'll call you as soon as I can.
I'll call you the moment/Instant I can (Sounds wrong)

Thanks in advance Emotion: smile.