site optimization can be done by yourself and also using a validator (http://jigsaw.w3.org/css-validator/ & http://validator.w3.org/).
SEO, just read up a lot on it and then you do it yourself, no program to do it. If you dont want to do it then you can pay someone to do it for you (make sure they know what they are doing).
Link checking - not sure where a site to do this is, but one way to help prevent dead links is to use relative linking instead of direct.
basically all you need is a text editor to do you code in, a graphic editor to do your graphics, and FTP to upload. hope this helps