Thank you.
I don't think either of these precludes putting money in index funds and forgetting about it for decades, which is what is being advised on this thread. The lack of menuchas hanefesh comes from trading stocks, and the other point about speculation is also not applicable to index funds that you ignore.
The "forgetting about it for decades" is the key. The way I understand the lack of מנוחת הנפש issue with stocks is the constant awareness of frequent price fluctuations. If the market were to drop 4% in one day, I am pretty sure that even a person that intends to "forget about it for decades" will think about it. Depending on what else is going on in that person's life, it might create more of an issue. If the drop continues, it is almost inevitable that mental energy might be spent pondering it. Whether fear of untimely losses, or greed of BTD, or regrets of not BTD or not selling some position at a certain point, and and all of those take mental space and energy, and I think that is the issue the Rebbe is referring to. And the larger the balance is, the more mental space it takes.
Full disclosure: I do have money invested in stocks in various types of accounts. I have one tiny HSA account in which my 1 year rate of return is triple digit. I took some risks there, got a little lucky, and timed some things right. Had I lost 90% of the value of that account I wouldn't lose a beat (though all along I had a significant portion of that account invested in a high dividend paying stock). But for my larger and more significant retirement accounts, there's much less risk taken, and returns are much lower accordingly.