I dont know how many times I have to explain this:
"privately purchased mutual fund" - yes though I have never heard a mutual fund(s) that ANYONE can buy through just about any brokerage firm as a private purchase
Paying 15% tax on capital gains - yes. You make money, you pay taxes. Making money and paying taxes on it is better than paying no taxes on making $0. Also, I think in your mind, you are thinking that if you withdraw $1000 per month then that's $150 (15%) per month in CGT. It doesnt work like that. When you make distributions from a fund, the largest portion, especially early on, is going to be a return of principal. So, just spitballing, maybe $50 of your $1000 would be a capital gain so you'd pay $7.50 in CGT.
Last point - you said its better to pay off your mortgage and invest that $1000 in some other type of investment. 2 things: 1. You are starting your investment at $0 instead of $100,000. $100K grows faster than starting at $0. 2. You are substituting your mortgage payment for an investment so your disposable income is the exact same. In my strategy, you have an EXTRA $1000 in disposable income per month because the mutual fund is paying your mortgage.
This, again, depends on each person's exact scenario. Generally, if your mortgage or student loans are less than 5%, it would probably (not definitely) be a good strategy to invest any windfall money instead of paying it off.