1. Absolutely not. Only harmful ops + military and market ops count toward spy dr. Standard spy, alliance spy and failed ops of any kind do not. There's a war tactic involving dumping 25 market ops on a waller to prevent bios. Kind of a big waste of turns tho. It does work tho. Drs tend to become obvious around op #25 on a single country assuming only harmful/military/market.

2. You can do 50 ops at 23:45 and then 50 more at 00:01. So yes.