1: Is it okay to install a 64 bit os with only 1g of ram or I have to install more ram to work on 64 bit os, and if not what is the problems will accure.
2: If I installed more 2g ram + the 1g that I have is it ok, because I heard that core2due prossesor want even number of ram to work well on 64 bit os (2g ram , 4g ram ,6g ram)

With respect to RAM, the 64-bit processor simply increases the maximum that can be directly addressed. There's no problem with installing less.

I don't know why this would be true---do you have a link or other reference?

Even number of RAM ? but 512 is even, and so is 128, 64, 32, 16, 8, 4, 2, so I don't get it. It's true 64-bit programs are larger and require a bit more RAM, but not that much, maybe 5-10 % more, almost negligible from what I've seen.

Even has nothing to do with the amount of RAM but with the number of sticks. If you want to take advantage of dual channel, then you need to install RAM in pairs. For example, 2 X 1GB, 4 x 1GB. The sticks in a pair should be the same size but you can have two pairs that each have a different size (2x1GB and 2x512MB for example).

I have 2X512 of ram with core2due intel 3.00 ghz so what is better for me 32 bit OS or 64 bit OS

I would recommend 32 bit. There really isn't much of a reason to use 64 bit with 1GB or RAM. Unless you are into databases, 3D, multimedia editing (in which case you'll want a lot more RAM), 32 bit is just as fast and it consumes less RAM (I have some reservations about it being just 5-10%; just run the free command right after booting the system and chances are you'll find that the 64 bit version is using 60 to 70% more).
Technically, a core 2 duo is a 64 bit processor but that's relative. Most 64 bit CPUs are not really 64 bit, they are just 32 bit with a few extensions latched on to add some 64 bit capabilities.

Ram is always even. Even number of bytes, powers of two to be more exact.

I don't know what are you talking about. Maybe you are confused by dual channel ram, or any other thing.

There's no problem using 1gb, 1.5gb or 256 mb of ram if that's what you have available.