Yes, you can still purchase new DVD and VCR combos. You can buy them at http://www.amazon.com/Philips-DVD740VR-DVD-VCR-Combo/dp/B00006ANZ7
Yes, you can still find DVD/VCR combos. Overstock.com has many for under $100. See http://www.overstock.com/search?keywords=dvd%20vcr%20combo&SearchType=Header for more information.
Yes, there are DVD/VCR combos available for the use in automobiles.
Most VCR/DVD combos come with a remote, and can be programmed to work with your TV remote.
Yes, Sony makes several versions of a DVD/VCR combo. These include progressive-scan DVD/VCR combos and DVD recorder/VCR combos. The latter is capable of copying VHS content onto DVD.
Yes, upscaling DVD/VCR combos are available for purchase.
No, they are not as good quality. I have gone through several TV and DVD player combos, all of which stopped working within a year. The TV and the separate DVD player I now have has lasted about 10 years.
Because the manufacturers are idiots!
Most DVD/VHS combos are now capable of recording VHS content onto DVD.
There are a couple of good options for kids TV/DVD combos. FAVI L 1818A-V-P 19' LCD HDTV TV/DVD Combo and Disney's 13' TV/DVD combo are both good options for kids.
TV/DVD combos are not very popular on the market anymore. They are becoming obsolete. However, if you want to buy one, they are still available in most stores such as Walmart, Target, and Kmart at a very low price.
While they make DVD/VCR combos that will play DVD-R and DVD-RW, there does not appear to be a DVD/VCR combo with a DVD writer available for purchase.