Please ensure that you have installed LSPDFR correctly, Rage doesn't seem to be able to find the LSPDFR files it needs as you have either not installed them or installed them in the wrong place. Please closely follow the installation guide and drag the entire contents of the download folder into the main GTAV directory.
Try reinstalling EUP Menu, as that is throwing an error. Can you please also describe the issue? Also, Increase your PluginTimeoutThresold to 60000, press the settings cog while loading Rage to change this.
What is the actual problem, i.e what is working and what isn't? Is your game crashing? If so, please upload the rage plugin hook log from the GTAV directory.
Please update LSPDFR to the newest version. Also increase your plugin timeout threshold to 60000, to do this press the settings cog when loading Rage Plugin Hook.
If your game is working with your mods folder named _mods but not as mods, then there is an issue in your mods folder causing the crash. I would recommend uninstalling all of your mods and starting again unless you know what ones you have installed since the last crash, in that case remove them.