You should install the patch. It will not cause a problem with existing saves, and in addition to bug fixes there are more graphics options, some balancing changes and a nightmare difficulty level added.
If you have D2:ED + FoV installed, then you only need to worry about the FoV patch (any changes to D2:ED are already included). If you have DKS, then it includes the remastered game and the add-on, so you only need the DKS patch.
If you have saves from D2:ED, you can load them and continue after FoV is installed. D2:ED saves are not compatible with DKS, so if you either have DKS or install the FoV to DKS conversion patch you will not be able to use any D2:ED saves.
I would assume the missing NPC problem starts off with the game itself, but if you save after it happens, the wrong location (or status, etc) gets written into the save file. The patch fixes whatever the issue was in the game that causes the problem, but doesn't check existing saves for the issue.
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