Can I connect a non-apple display to my mac mini

1. See #2.

2. It depends on what type of cable the monitor has and the Mac mini’s ports; there isn’t a difference between an Apple and a non-Apple monitor for this purpose. A Mini DisplayPort adapter can be used to hook an older display up to a Thunderbolt port.

(142062)

Yes.

Standards like VGA, DVI and HDMI will work with every monitor that has a VGA/DVI/HDMI port.

I recently found that newer versions of OS X (El Capitan?) did not show all the graphics modes, and refused to show the monitors native resolution while connected via HDMI. (My monitor has a resolution of 1680x1050. With HDMI only 720p and 1080i/1080p was shown.) The resolution is to use the Option key while clicking on the "Scaled" option, as described here: https://support.apple.com/kb/PH22157. Then simply select the native resolution of the monitor and everything is fine.

With Thunderbolt everything could be different.