Foxconn LGA775 windows 7 + best processor

Solution
You don't have an Intel motherboard. You have a Foxconn motherboard with an Intel chipset. The specs state that you can use that RAM: http://www.foxconnchannel.com/ProductDetail.aspx?T=Motherboard&U=en-us0000343
It appears to be low-density, which is probably correct for that older chipset.

One other caveat... check the version of your motherboard BIOS. You may need to update it to a later version depending on which of those faster CPUs you find available.

Btw, I have no idea what the thing about the memory controller is you want to check, since you don't have an AMD CPU. You have an Intel CPU. Older Intel CPUs like yours don't have an integral memory controller. The memory controller is part of the motherboard chipset, unlike...
Currently there is Intel pentium 4 521, 2800 MHz (everest).

I'm not sure for the FSP= 1333MHz because undet the specification tab is says *oc for 1333 (Front Side Bus 1333(oc*) / 1066 / 800 / 533 MHz (FSB))
 
How can I check this?

"In case you did not know, the memory controller inside AMD's CPUs supports addressing of 11-bit columns while using 16K page size. In comparison, standard memory controllers on the market support 10-bit columns with 8K page size. In addition, AM2's controller can support as many as 2048 individual entries if a page size is 16Kbits, allowing the controller to stay longer on the same page."

to see if I can use this memory with my motherboard:
http://www.ebay.com/itm/2-x-2GB-2G-RAM-DDR2-PC2-5300-U-667MHZ-DIMM-Memory-240-Pin-PC-Memory-D2M-/221996080466?hash=item33afff5d52:g:R0wAAOSwGotWmUWv

How can I know if the ddr2 is suitable for my Intel Motherboard?
 
You don't have an Intel motherboard. You have a Foxconn motherboard with an Intel chipset. The specs state that you can use that RAM: http://www.foxconnchannel.com/ProductDetail.aspx?T=Motherboard&U=en-us0000343
It appears to be low-density, which is probably correct for that older chipset.

One other caveat... check the version of your motherboard BIOS. You may need to update it to a later version depending on which of those faster CPUs you find available.

Btw, I have no idea what the thing about the memory controller is you want to check, since you don't have an AMD CPU. You have an Intel CPU. Older Intel CPUs like yours don't have an integral memory controller. The memory controller is part of the motherboard chipset, unlike AMD CPUs.
 
Solution
I would honestly suggest you save up for something better rather than spending money further into your current motherboard, since it doesn't even support the Core 2 Quad series. Maybe if you had another LGA775 motherboard, it would be worth upgrading...
A Core 2 Duo is as high as you'll get.