I would like to know if anyone knows how a person can obtain a deceased family member's citizenship papers if they don't know the names of that person's parents. Also is there any other way that I can get anything that may have that persons parents names on it, and how do I get it?

As far as I know parent's names aren't required to obtain citizenship papers - it's the information on the person in question that's important. Their full name, dates, proof of death, and if the death is recent proof that you are next-of-kin.

Birth and marriage records would both include the names of parents, and depending upon year of death (after 1907) death records should also include this information if it was known to the informant.

I would like a copy of my ggfathers naturalization record. I have all the information plus the naturalization number. So in a sense, it really isn't a search. Would I still have to pay the $75.00 they require to do a search?

According to the CIC Fee Schedule the fee for a search and the fee for a certificate without search are the same.

2010 Update:
For $5 you can apply for and receive Naturalizations Records between the years 1915-1932 using the LAC online index. You will have to provide proof of death when applying.

Is a child of Canadian citizens, who was born in the US a Canadian citizen?

From Citizenship & Immigration Canada -- In most cases, you are a Canadian citizen if you were born: in Canada ; in another country, after February 15, 1977, but had one Canadian parent. You may be a Canadian citizen if you were born outside Canada before February 15, 1977, and one of your parents was a Canadian citizen. For more information you may telephone a Call Centre: In Montreal: (514) 496-1010; In Toronto: (416) 973-4444; In Vancouver: (604) 666-2171; For all other areas: 1-888-242-2100

What were the requirements for citizenship in 1910-1920? Specifically, how soon after immigrating could someone begin the process, and how long would it take?

Canadian Citizenship wasn't established until 1947. Prior to that time, any British subject (those born in the UK, Canada, Australia, etc) was able to travel freely between British colonies without documentation. Those immigrating from other countries were naturalized, something they could apply for after living in Canada for a minimum of three years. For more information about this please see links