Latitude 5420 SIM slot

1.  You need a SIM card and a WWAN adapter.  If the system shipped without the latter, the antenna wiring likely is absent (and would require a replacement display panel to install).

2.  Standard SIM.

3.  Depends on the WWAN card you choose;   you'll have to ask your service provider what they support.

4. . Yes.

From image you have in your post it's clearly visible what WWAN module is missing (not installed) as well as there's no retention bracket/screw and highly likely LTE antenna cables are not installed too (they would normally be visible hanging inside upper side of WWAN M.2 slot near screw).

Therefore whatever SIM card you put inside that SIM slot - nothing will happen because processing module (hardware) is missing.
Compatibility of WWAN module (not only hardware but on Firmware/Software levels, hardware is normally fine but firmware/software configuration often needs to be matched) with your local mobile service providers is a bit different story, there are different bands, reception zone, signal standards, etc. (also each WWAN module normally has IMEI which should be accepted {not blacklisted for some reasons} by service provider).