From your description I can assume that the added "plates" are drawing figures assigned to the Signal/Plane layer on both sides of the board. In this case, make sure all of the vias belong to the same net, then do the same for the new Signal/Plane drawing figures. Once that is accomplished, those er...

Are the "plates" copper pours? If so, were they updated after adding the vias?

With the search filter still open, hover the mouse cursor (do not click) over a component name in the list of found items and a pop-up will show the related library.

Assuming you're using DipTrace v4.2.0.1, turn on all layers (right side of screen) to see if there is anything blocking the trace from being completed... As a last resort, you can disable the "[ ]Follow Rules" option in the "Routing" panel on the left side of the screen...

Can you post your pattern library (*.lib) here for examination by others?
Does the stock DipTrace component named "87758-0451" do the same thing on your system? I am unable to replicate the problem using v4.2.0.1.

Right-click on the pad and select "Thermal Settings..." in the context menu.

...Is there a way to permanently disable it for a part, or do I create a new part?...

I think you will have to create a new part. You might want to assign a blank STEP file to it if only to keep the 3D Preview tool warnings to a minimum.

DipTrace version 4.2.0.1... ...How do I route a trace and drop a via to hit a pour and complete the routing?... Routing a trace can be initiated by pressing the " ~ " (tilde) hotkey. Make sure the copper pour has been assigned to the same net as the trace in question. In DipTrace you will have to fi...

I don't remember. In the distant past I think I was able to load the new version beside the old one, but I can't be sure. There may have been some shared DipTrace system files that were updated which could have caused some problems with the original installation. Just for the sake of a fresh start, ...

For what it's worth, here's an older thread with a conversation about upgrading from 3.x to 4.x - https://diptrace.com/forum/viewtopic.php?f=20&t=14447 As far as backward compatibility goes, I wouldn't rely on it. If I remember correctly, it might be possible to export a 4.x design to a DipTrace ASC...