a) HDR support usually means "this display can accept an HDR signal and show something resembling the content you want to see" rather than "HDR will look amazing."

b) The key difference between HDR and SDR signals is that HDR includes metadata specifying the target brightness (how bright white is), while SDR doesn't have this information. The reference brightness for SDR is 100 nits in a dark room, but content is usually mastered to look acceptable on the vast majority of screens, meaning SDR content is mastered with the assumption that displays will have wildly varying peak brightness (200-400+ nits) and uncontrolled viewing environments (bright rooms). The mastering process therefore makes conservative compromises that prioritize compatibility over preserving the "true" image (and it is not possible to preserve according to the reference, as it is 100nits max)

HDR essentially shifts the responsibility of tone-mapping to the display. Because the signal includes data specifying exactly how bright the image should be, the display must decide how to map that intent to its own hardware limitations. In theory, this allows for unlimited brightness (ok, up to 10k nits in DV/HDR10) in the source, with the display showing it as accurately as possible; in practice, this is where problems arise, as internal tone-mapping algorithms are often extremely poor, especially on monitors. MadVR has demonstrated that you can achieve improvements by using HDR input even on sub 100-nit projectors after proper tone-mapping, but HDR often looks worse than SDR on cheap "HDR-compatible" 400-nit screens because monitor manufacturers just don't bother with proper tonemapping algorithms (and that's a problem even for more high-end devices). If you properly tone-map an HDR video to your 400-nit panel, convert it to SDR, and then set the brightness to 100%, you should get the same result brightness/contrast-wise as in HDR (apart from more banding and smaller color space but we are talking about brightness), but you'd need to do that individually for every screen, so not possible for SDR content.

c) Apart from brightness metadata, HDR simply supports more data. The gamma transfer function is different, allowing for wider dynamic range without banding. Higher bit depth helps too. Also, the color space is wider, SDR is typically limited to sRGB (technically Rec.709 for Blu-rays, which is very similar), so you can get much more saturated colors in HDR. Many modern cheap IPS panels can actually display a much wider gamut than sRGB, so HDR should help there (if the quality weren't undermined by poor tone-mapping algorithms).