I usually use the "next ship" and "next fleet" buttons (upper right corner; I forget the hotkeys) to cycle through all my ships/fleets without orders. You might want to check the options (i.e., which ships/fleets the next ship/fleet button will skip; for instance, you can set the next ship button to skip ships in fleets) to make sure you're comfortable with how it works.
I also recommend checking the "empire status" every turn, so you know how much surplus (or deficit) you're creating; if you have a large surplus (or a large deficit), check your construction queues; don't forget to check research and intelligence every turn as well. Oh, and if you're building lots of units (fighters, satellites or mines in particular), go to the "colonies" screen and check planetary cargo; that will help you remember to load/launch those units (or, if planetary cargo is full, to stop building).
The best thing is to come up with a system. For instance:
- Check turn log, paying particular attention to notices about unit construction completed
- Update ship/base/etc. designs based on newly completed research projects
- Check intelligence projects (particularly counter-intelligence)
- Cycle through all ships
- Cycle through all fleets
- Check colony screen for "mood" (jubilant, happy, indifferent, etc.)
- Check empire status
- Modify construction queues (especially if you have new ship/base/etc. designs that should be put into production)).
I've probably missed something, but those are the basic things to check. And, as some people (like myself), things to double- and triple-check. 
Re: Some basic questions
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