You can only contribute £40,000 per annum to your pension. However if you've not contributed that amount in the most recent 3 tax years you can carry over your unused allowance and therefore contribute more than £40,000.
If you exceed your allowance you'll need to pay tax on the excess which rather defeats the purpose of your contributions.
You must ensure that you're at least paid the UK minimum wage so if you only earn £40,000 you can't contribute all of it to your pension.
Your personal allowance is the amount of your earnings that you don't pay tax on, you can contribute that to your pension (subject to the minimum wage rule above), but there's little point as you're not saving any tax when you make that contribution.
The investment options you have available are specific to the pension scheme you invest in. You may be able to invest in US capital markets via a US fund, you're unlikely to be able to invest in specific stocks unless you have a personal pension and manage it yourself though.
It depends on your age when you can start making withdrawals from a personal or private pension but you'd usually need to be at least 55 years old and potentially a year or two older than that if you're under 50 right now.
The money you withdraw is taxed as part of your normal income, usually you'd pay a lower rate of tax because your annual pension income would be less than your annual earnings prior to retirement.
You'd need 35 years of contributions to qualify for a full state pension currently. You can look up where you are on the government's website. The minimum number of qualifying years to get any state pension at all is 10.