For mods that are only compatible with a particular KSP version (eg Kopernicus, and probably some of the visual mods you are also having trouble with) you first need to get the version of the mod that matches your version of KSP. (As far as I'm aware virtually all mods that work on modern version of KSP will work correctly with 64bit, so 64bit shouldn't be an issue. Indeed if the mod author say a mod is compatible with 1.5.x, then by definition it needs to be 64bit compatible, since there is no 32 bit version of 1.5.x).
Once you have your mods working, you also need to make sure that Steam doesn't update KSP, because an update will mean that the mods, (and hence any saved game that depends on those mods) will break. (If that happens with a game that uses Kopernicus, then since Kopernicus is used to change/add new/different planets/moons to the system, any satellites/ships that orbit any of the changed planets/moons are likely to have their orbits disrupted, which pretty much wrecks any ongoing missions). The simplest and most effective way to do that is install your mods into a copy of KSP that isn't under Steam control.
It wasn't (and still isn't) clear whether you were having problems getting Kopernicus working with 1.5.0 or 1.5.1. (You still haven't answered which precise version of ksp you first tried. You did mention trying 1.4.4, but it isn't clear what version of kopernicus you tried to use with KSP 1.4.4. (As far as I can tell there was no Kopernicus release that is compatible with KSP 1.4.4)). Many planet packs that depend on Kopernicus will probably work with 1.5.1, once there is a compatible Kopernicus release. In the meantime, you can wait, or you can rollback to KSP 1.4.5 and use one of the kopernicus releases that are compatible with 1.4.5. (eg https://github.com/Kopernicus/Kopernicus-Backport/releases/tag/backport-1.4.5-5 or https://github.com/Kopernicus/Kopernicus/releases/tag/release-1.4.5-4). (Technically there is a third choice. If you have the development skills, you could download the source of Kopernicus, make the necessary changes and then build a version that is 1.5.1 compatible. But if you do that then don't expect any support from the mod author, and don't distribute it to other people, unless you are going to provide them with support).
Copying KSP to another directory won't magically help you get those mods working, but it will help you keep your mods working, by preventing Steam from updating KSP, and was just general advice to anyone who seems new to dealing with version locked mods.
TL;DR You need to get version of your mods that are compatible with your KSP version. For Kopernicus that means either waiting, or rolling back to 1.4.5. At a guess the visual mods are probably similar.