Both of those problems can be solved if you just do it slowly in a pre-announced manner. A trillion is a thousand billions, so you could cash out 1 billion dollars annually until the 30th century assuming zero growth/inflation. So unless you're really worried about the optics of selling 0.1% of your holdings, or plan to spend more than 1 billion a year outside your business, you're not really constrained.
Everything is liquid in a long enough time horizon. It just depends on what you mean by liquidating. Like do I have to sell my house today? In a week? Months? More flexibility = more value.
For Musk the situation is definitely more extreme though. Since a significant part of that valuation is attached to him owning it, he would definitely take an abnormal level of haircut. Probably an unknowable investor sentiment question though.