It sounds like you guys are having the same issue I had a while back with LootingBots and QuestingBots but yeah remove LootingBots the next time you are able to and go from there. I am 90% certain this could be the mischievous mod lol.
To answer your question; if you delete a mod that has no other dependencies for it (like for example, a mod requiring another mod for it to work or to add more content for the game) then there should be no issues. On the other hand however, if you have any active armour or weapon mods and you suddenly remove it whilst wearing/using those mods that could potentially cause issues so remove any armour and/or weapons from your inventory and stash prior to uninstalling as to not break your game. Just some friendly advice, always double-check the mods you use just in case things change or get updated and read the mod page information properly. I see it time and time again from other users who don't take the time to read things properly when things go a bit awry, it will save you a heep of time and less headaches. Hope this helps!