I will be going down your list one at a time:
PC Response Moderation works on the Endar Spire currently, not sure how far beyond that it goes, and I'm not sure if its changes would be overwritten by K1R or not.
Party on the Leviathan has a slight oversight in the installer that I will be patching shortly, but there is a script in the tslpatchdata folder called "k_plev_freecs2.ncs" that will need to be manually moved to the override folder.
I am not sure, but the Endar Spire dialog should be good to go for K1R.
At this time, NPC Overhaul is not compatible with K1R, due to shared level files and NPC Overhaul doing all of its changes inside the actual levels themselves and then replacing the .mod files already in the modules folder if they exist.
On the Vulkar Coward Redux, that's up to you. I think the pure vanilla option doesn't actually work with K1R, though. Basically, if you want the guy to look and talk like a Twi'lek instead of looking and talking like a Human (as is done in K1R), use this mod.
Ord Mandell is a fun mod, and definitely will keep up with challenging you. I haven't installed it in a while, though, so I forget how it installs. Same with Yavin IV.
The next four mods I've either only used once (the Korriban Crystal Caves mod) or never (the rest), so I can't really speak on them.
The entire Character Models section should be fine, but pay special attention to what Darth Parametric said.
Honestly not sure how the Bastila Romance Enhancement will play with K1R, since I believe ZM90 edited her dialog file.
The Sunry Murder Recording is already integrated into K1R.
Black Vulkar Soundfix should be safe to use.
The Cutscene mod is not actually cutscenes. It's editing the audio of the videos the game plays, but that should be safe to use.
I'd be careful with the Korriban Workbench, as I recall talking to the author about it once, but I forget if that was in relation to K1R or not...
Never use the Xia Tarashei mod.
I am not at all sure how the K1 Enhancement Pack's stuff will work out.
Weapons of the Old Republic will probably overwrite a bit of the stuff from Weapon Models Overhaul and the Vibrosword mods, and you will need to delete several .utc files (I'm not sure which ones, you'd need to ask Malkior) to work on the Leviathan and some spots afterwards.
Not sure about Xiskio's Holster mod.