She still exists. Just that he can't listen or understand her thoughts like he could when he was connected to her as Puppet Master

They couldn't buy the sword because they didn't have that much money when they were new and in Bloodline Trials and the sword was only sold the Bloodline Trial.

Multi-billion dollar means the turnover of the company is in the billions, not the profit or cash at hand.

When he first entered teg Rest Hall but snuck out when everyone else was fighting and trying to stop each other

It won't work on the potions and elixirs. The reason potions work for a small duration is because that's how much essence they contain. If a potion is suppposed to work for half an hour, then it means it'll be exhausted after half an hour completely. Its's not because they have limit on them. It's mainly because of what materials were used while making them, and how much essence they contained which determine how long they can work before they're completely exhausted from the system of the Player. As for your second question, as the other commenter mention, the skill limits can potentially be removed, like the cooldown of his footwork skill was removed. However, Limitless is a passive skill and MC can't control or willingly use it yet. So in the potential future, it should be possible to remove cooldowns, though there are still some problems in Bloodline Specific skills that might be explained later.