1) Most of the lack of quality is in the source. Not only is that small but it also has a lot of artifacts. Increasing the size AND using noise reduction usually doesn't work well.

2) That's more than 2x. If you're going to increase the size, just use 2x. The larger you make it, the more the flaws and lack of detail stands out. Images here don't need to fit a standard resolution or AR.

3) A good scan source will have a very large resolution and little to no JPEG artifacts. Losses occur during printing and scanning. So when scanning, care should be taken to preserve as much of the quality as possible. If you ever have a scan that's too small for this site, that's a bad source.