I am wondering if I should buy a Sony α230 DSLR. My price range is $500. Does this camera have a removable lens, or a fixed one?
What are pros and cons of this camera model?
Not that is anything wrong with the A230, all recent DSLRs are good and feature interchangeable lenses.
Only the A230 is discontinued. Sony's new sensors give much better image quality in low-light and they do have several models within your price range: Sony A290 goes for under $400. They also have the A390 which costs more but with a smaller viewfinder and live-view instead, the rest is the same so the cheaper model leaves you more money for lenses, which is more important.
There may be other brands too but not many models under $500. Since Sony makes sensors for almost everyone except Canon, expect image quality to be similar among cameras of the same generation. The biggest different is which lenses you can attach and that Sony cameras have built-in stabilization (like Pentax and Olympus) which gives you that feature for free without paying more money for stabilized lenses.
Yes, it has an interchangeable lens. The mount is compatible with all Sony and Minolta A-mount (Maxxum/Dynax/Alpha) lenses (and, of course, there are compatible lenses from the usual third-party manufacturers like Sigma, Tamron, and Tokina).
I haven't used one enough to really many much in the way of recommendations. I did play with one a little bit, and didn't find it particularly comfortable -- the grip didn't fit my hand very well. I should add, however, that I'm mostly accustomed to Minolta/Sony 9-series cameras, and normally (always, really) use them with the vertical grip installed. This has probably warped my perceptions of what to expect as far as the size/weight of a camera goes.
I would recommend you go to one of the popular forums like DPReview where you will get much more information.
Here is the DPReview.com review which is closest to your camera.
And here you can ask question of the many enthusiastic users of these cameras.
Disclaimer: I have owned/used Minolta film cameras for several years.