How can I ensure that scrambled eggs will be fully cooked?
Temperature is the only foolproof way to determine doneness. Unfortunately it's not very practical to carry a thermometer over to your friend's house for brunch. 

There are other indicators, of course, and you have mentioned the good ones for eggs.

I will add, however, that some indicators can be deceiving. For example, eggs releasing a pool of liquid is actually a sign of over-cooked eggs. The protein matrix is tightening to the point that it's actually expelling water. This is different than runny, uncooked egg. 

Similarly, browning isn't necessary for the cooking of an egg (frankly, it's often detrimental). So while browned egg is likely more cooked than not-browned egg, it may also be less done on the inside.

They are clues you can use to identify doneness but none of them are guarantees.

I'd suggest sticking to fried eggs if that's what you enjoy and are more comfortable with.  

So to answer your enumerated questions directly:

1) Scrambled eggs cooked to a typical doneness are moist, not-browned, and not expelling excessive liquids on to the plate. If the eggs are not done, they will not be "set" into curds and will be noticeably slimy. 

That said, cook them how you like them. 

2) Cooking time is dependent on cooking temperature. It's really not a good way to judge doneness. It works better for large cuts of meat or something that will take a lot of cooking time. An individual egg cooking time will vary. Yes, adding additional ingredients (mass) will slow it down.

Overall it will take just a couple of minutes tops. If you start with a hot pan, you can scramble an egg in just a few seconds. 

Note: I'm talking about the scrambled eggs you typically see in American diners that look similar to the photos you posted. French style scrambled eggs are creamy in consistency and lack the large curds. Doneness is a little more difficult to judge in that dish.