Do I have to install a seperate conversion tracking snippett for each adwords campaign I run? Or do I just need one code snippett for all my campaigns? I haven't figured out if its per adwords account or per campaign.
Nope, you just need to one code and it will work for every Campaign related to that website. For the future, you need different code for each website and/or type of conversion (for example, selling a product and then someone filling in a contact form).