Are those other planets or other stars? Or is that a lens effect?

Looks to me like a planet and some moons. I don't know where you are, but Jupiter has been very bright in the night sky lately in my neighborhood, and with a long enough lens it's not hard to see some of its moons.

Seen through a sufficiently powerful telescope, a planet looks very different form a star. Stars are brilliant, like diamonds. Planets are round and less brilliant, what you'd expect from giant spherical rocks that aren't on fire. But most camera lenses don't offer enough magnification to let you tell the difference, and because planets are relatively close they're often the brightest things in the sky other than our own moon, so they're usually overexposed in your photos.

Perhaps the easiest way to figure out what you're looking at is to get an astronomy app for your smartphone or computer. I use Sky Guide on my iPhone, which uses the phone's compass, accelerometer, and GPS to show you the part of the sky that the phone is pointed at, which makes it very easy to find the objects that you're interested in. And you can change the time and date that it shows, so you can see what the sky would have looked like 3 days or 100 years ago or in the future. If you can remember the direction in which you pointed the camera and read the date from a photo's EXIF data, you should be able to figure out what the objects in your photo are. Well worth the $3 price.

In the past, I've used Starry Night on my laptop computer, and it offers similar capabilities as Sky Guide. There are probably some other good software options as well -- the main point here is that there's software out there that makes it easy to figure this stuff out.