I have funds in a 401K plan from a period of time I worked in the US in the late 80s. I am not a US resident and I wonder if at the age of 60 I can start monthly withdrawals and how are these withdrawals going to be taxed in the US.
Yes, you can take monthly withdrawals (they are called "distributions") when you're 60.
If you're a US resident these funds are taxed as if they were wage income.
At your death, many years from now, any remaining money is considered part of your estate.
If you live outside the US the situation is complex. It depends, among other things, on treaties between the US and your country. You should call or write to the distribution department of the financial institution holding your 401K. It is their job to help you sort this out.
You will be able to withdraw them, and they will be US-sourced. I.e.: you'll need to file a non-resident tax return and potentially pay taxes on the income (if it is substantial enough). Your home country may have a tax treaty with the US which may affect how this is treated by the US or your home country. Your home country may also have foreign tax credit to allow reduction of local taxes on the account of the taxes you paid on this income in the US.
You should talk to a tax adviser familiar with your home country rules and the US rules, and especially if there's a tax treaty between the two.
No, the 401k custodian will not help you, and will not know what and how you should be doing. They'll just know to send you a check if you ask them to.