How long should I wait before asking about the burial plans?

Is the friend you say you are caring for? Is he an only child, if not I would think someone has taken on that responsibility. If the father was on Hospice, his body was taken directly to the Funeral home of choice. I hope that knowing he was passing he made prior plans with the Funeral Home. You can prepay a funeral. A regular burial is 3 days. Cremation is a little different. A viewing may be done for immediate family. Cremation is usually done right away because there is no embalming. Family may choose a time in the future to have some kind of service if at all. Depends on the wishes of the person who died.

What you can do is ask if there is anything that you can do to help your friend or the family.
Bring a dish that can be heated up easily or frozen for later.
If there is a lot of family a tray of cookies, maybe a tray of cold cuts and bread or rolls. During any other time I would suggest Home Made goodies but not now, store bought is the safest option some people are hesitant to eat foods made by someone.
Just continue to be a good friend and offer support.

Here is the original poster's (OP's) other post:

"my friend lost his father today to cancer. He knew his father would not last this month, as a friend who cares what should i do??"

I do not see anything in your profile other than you are caring for a friend 25 years old.
If this is the person you are talking about and they are dying you should be able to talk to them anytime about what they want.
If they are on Hospice this might be something that you, your friend and the Chaplain or Social Worker can talk about.
If it is talking to the family if you know what your friend wants please tell them specially if they are talking about doing something that you know your friend would not want. Some people do not want to discuss this at all. My Husband never talked about it and would get upset. It was not until I talked to his sister that I found out that he wanted to be buried next to his mom.

Since you also asked about how to be a good support, how about asking "you must be super busy making funeral plans. Can I help out in any way?" Or ask specifically if they need help walking the dog, staying at the home during the service or bringing food.

In my community's tradition, you just show up with a cake or a casserole as well.

Are you asking the remaining family or are you asking the person who is dying?
Either way, do it quickly. (but not on the day of death...grief and all)

We made all arrangements a year ago for 98 year old Mom and paid in full. It locked in a price and allowed us to make decisions that would be even more challenging at the 12th hour. It’s never easy.