Evidently.
I don't know which lens you're talking about, but I'm willing to bet it's a mirror lens. One that's 600mm f/8 and then they add a 2x tc to make it a 1200 f/16? You're not likely to be happy with it, although you might get some moon photos you like out of it. But generally, you get what you pay for, and a $200 1600mm lens that you can't control the aperture on and that doesn't autofocus probably wouldn't seem like a bargain to most of us. Unfortunately, with optics, you do get what you pay for.
Well, you've mentioned what you'd like to do, but what do you NEED to do? I only know Canon gear, but if you really wanted to devote about 90% of your shooting to astronomy shots, I'd say maybe a 60Da body. But that's about three times the cost of your A3000. And we haven't even started looking at lenses yet.
I may be wrong, but if one of the reasons you were attracted to the A3000 was the price, chances are good that what you want to do isn't going to be compatible with your budget. I generally tell people they'll need $2k-3k to outfit themselves with a body and three or four lenses. Having additional interests like macro and supertelephoto just add to the cost. You can do things for cheaper, but you're going to lose functionality and handling capability. Probably not image quality, though. The difference between lower end and higher end bodies are typically those of usability features. A lot of camera bodies in a lineup will share the same processor and sensor, so they tend to share the same image quality.
Key word "appears". While it's touted as a 24-1000 equivalent lens, it only manages that because the 1/2.3" sensor has a 5x crop factor. The
actual focal length of the lens is 4.3-180mm.
Also you probably want to stop using "zoom" as a term that means a lot of magnification. Zoom in interchangeable lens terms typically only means a lens that can vary its focal length. The Tokina 11-16mm, for example is an ultrawide zoom.
Yup. It takes a while to wrap your head around all of this stuff. But you may want to start before you make any other purchases that aren't going to fit what you want to do. My advice would be to figure out what your A3000 can do, and then work to its strengths, and do some research on the lenses it can use, and how they'll work. You may not have a supertelephoto wildlife camera, but it's probably very good at landscapes, macro, and portrait.
Actually, you kind of can't. With a very small lens and sensor, as with most P&S cameras, you have a very very deep depth of field, and everything's in focus. It's very difficult to blur the background and to select only one thing in an image to be in focus. While you have a lot more in focus, you actually have less control than with a larger-sensored camera. Very tough to do something like this, where you can choose exactly what's in focus and what isn't:
Canon XT/350D. EF 135mm f/2L USM.
Whether being able to get things out of focus is a feature or a bug is up to you and the type of images you want to make.
Then don't buy just yet.
Learn about lenses. Learn about things other than mere focal length. A lens's max. aperture, whether it's a prime or a zoom, what kind of focus motor it has, what other shooting features it encompasses, whether or not it's stabilized, etc. all make a difference in terms of character, cost, and usefulness. Buying a lens is kind of like buying clothes: there are no "bests" that fit everyone. It all comes down to budget and what/how you want to shoot.