For TV #1)
I think you need to program your VCR to record channel 3 or 4, depending on the channel your converter box is set to. The output of the converter box should go to the VCR's input, and then the VCR's output should go to the TV.
Keep in mind that your VCR has an old analog TV tuner built into it that does not understand the new digital signals. The VCR must rely on the converter box to tune to the digital TV channel and convert it into an analog signal your VCR understands.
You will need to program the converter box to auto-tune to the shows you want at the dates/times they come on. You then also need to program the VCR to record channel 3 (or 4) at those same dates/times. With both devices working together, you can get your favorite show to record correctly.
For TV #2)
Could you check to see if the tuner is set for "Air" or "OTA" mode as opposed to "Cable" mode? The frequency assignments for over-the-air TV channels is different than the ones used by cable systems, so if it's accidentally set to CATV mode, it might be scanning the wrong frequencies. In the "Channel Setup" menu, there should be an option to do an "Auto Preset Ch(TV/DTV)".
It is possible that the tuner chip in this TV is not as good as the one used in the Zinwell converter box. After all, this TV was built to be as cheap as possible for its product niche, and it was also built using slightly older technology (circa 2006, compared to Zinwell's 2008 technology). Your TV signals appear to be very strong, but you probably live in an area where buildings bounce the signals around a lot. This can create a condition known as multipath (seen as "ghosts" in the days of analog television), which can make it difficult to lock on to a digital station. Newer tuner chips do a better job of coping with multipath than older tuner chips, so that might explain the difference that you are seeing between the two tuners.
If you plan on keeping this TV, you might be able to reduce the severity of the multipath by using a different antenna. A more directional antenna like the Philips PHDTV3 or Terk HDTVi (do not use the HDTVa amplified version) is more selective about which directions it picks up signals from. This can help clean up some of the multipath that makes it to the tuner because the antenna can screen out some of the reflected signals coming from unwanted directions. If the signal is sufficiently cleaned up, the tuner in the TV has a better chance of locking on to your channels.
Another way to reduce multipath is to get an antenna on the roof, if possible. A roof-mounted antenna is usually going to be out in the open and above most of the objects that cause multipath reflections. This is a much better way to get a clean TV signal, but might not be a viable option for everyone.
If you are willing to consider an antenna on the roof, you may want to familiarize yourself with the FCC's over-the-air reception devices rule (
OTARD), which basically grants everyone the right to install a reasonable outdoor antenna for TV reception. Since it is a federal rule, it carries the legal weight to override any landlord, HOA, city, county, or state rule (with only minor exceptions) that might otherwise restrict you from exercising this right.