1. Yes - I was under the impression that a person with a right to be a USC should travel on a US passport. This is what we've done with my son who is a USC via my citizenship. My husband is a UKC.
For my son, we have a cash Junior ISA which is fine for tax purposes in terms of avoiding the PFIC. Just note that any interest is taxable in the US, though this should be well under the threshold for IRS reporting considering the poor interest rates at the moment (unless you have loads of cash to save!!). I have not had to file an IRS return for my son yet, though he does have more than $10k so I've reported his accounts on FBAR for a few years now. His JISA account is with NS&I and they were OK with taking him as a US person. Many places are not, and this is a pain for both of us.
In terms of investments, I did have a JISA invested in funds but realised this was PFIC and therefore very unfavorable for him long term. I've sold the investments and it's just cash now until I work out what to do. If I were to do this all over again (he's 16 now), I would probably invest for him in my husband's name as a UKC and then work out how to give him the cash at some later date. JISAs are always inaccessible until they are 18, regardless of their nationality.
As a USC, I've found it tricky to invest from the UK. I haven't lived in the US since I was 21 (am 45 now!) so I have no financial ties there and can't open a US brokerage account. There used to be some US ETFs that were also UK reporting, thus avoiding problems both ways....but these aren't available anymore in the UK due to some EU regulations. I now invest in individual shares with Hargreaves Lansdown who were one of the few UK brokerages that would take me, and keep careful records of this for my tax returns. If you have $25k to invest, you can use Charles Schwab UK to invest in dollars in the US stock market. Again, I believe this is only individual shares rather than funds/ETF.
Good luck! I sometimes regret inflicting USC status on my poor child
.