"Send it to me after 10:00 on 7 Aug" is correct. This means on the date of 7 Aug, after 10:00 in the morning. The second one "Send it to me after 7 Aug at 10:00" means AFTER 7 August at exactly 10:00 (so on 8 Aug???) it's very confusing. You could also write "Send it to me on 7 Aug after 10:00" That order doesn't matter but the prepositions DO matter to explain (on, after). Let me know if you have any other questions. Happy learning!

It is unusual to tell someone such precise timing instructions, but as long as you are being so precise you might specify whether it is the time of sending or the time of receiving that is in question. If it is the time of sending, say "Post (or mail) it to me after ..." If it is the time of receiving, say "I need to receive it after ..."

There are some regional differences here. If you're talking to a US audience, they are more accustomed to saying Aug 7, and may get confused if you use post as a verb to mail something.

...or 10:00 pm if you mean the evening.

The first way sounds better. I would add 10:00 am.