Absolutely not for profit, there are a small number of employees (about 8?) which isn't bad for an event that had 30,000 runners last week. There are about 2000 volunteers each week.
Paul S-H invented it and could probably have made a load of money from it, but effectively gave it away by creating a trust or something like that to ensure that it can never be sold or make money for anyone else.
parkrun are very keen to protect the brand so if someone was trying to set another event up that deviated from the basic principles (Saturday, free, open to everyone, 9am in England, other countries vary) they would not be allowed to do it if they were trying to associate it with the parkrun name.
It costs a few 000 to set up a new event, this is half paid by the main sponsors and half raised locally - we had that from the council.
You will never be asked for money, but there is (if you can find it on the webpages!!) an option to donate, most of this goes to your local event and a small amount (10%?) to the new events fund - details are shown here http://www.parkrun.org.uk/aboutus/donations/
Finally, yes you should volunteer, it's good fun, you get to know people and runs can't happen if you don't, you can run 49 times a year and volunteer the 3 when you have race that weekend or are injured or had a late night on Friday! There aren't many things in life that you can give 3 and be given 49 back!