Your website would probably be a violation of the CFAA, the federal laws that make it a crime to have unauthorized access to a website or server. And yes, there would be multiple violations of copyright. Websites set up their own services and TOS how they want them. However, there are web app developers that gather around other services, but generally, they are only allowed to interact with a site if they are approved and nonharmful. If you want to have an app or service that interacts with a website, you have to strike a deal with the website, otherwise, you are likely criminally accessing their site and server.
Your first one, about uploading different size photos to a website than the site itself allows: Most sites are designed how the site wants them to be. There may be other issues involved, such as the width of other things on the page, the desire to have all photos match in size for nicer layout, the desire to limit storage space, etc. So they probably do not want you monkeying with that.
Your second example, of cloning peoples' photo albums, violates their copyrights, privacy, and other rights. It may also be a criminal violation of privacy laws.
Your third example, of handing bonus points outside the system of the website, would be a violation of their TOS as well as unauthorized access under CFAA.
My conclusion is that your plan would be civilly and criminally illegal in many ways. However, if you use the same technology to create desirable apps that interact with sites that approve of the interaction on their site, then you have a marketable plan. The apps are not likely to be legal if they violate copyright or privacy laws. If you are actually capable of developing such services, then work closely with a lawyer.
Some apps are used by users of big sites, but do not actually interfere or interact with the site itself. But, it sounds like the ones you have mentioned would interact. For example, bitly came out as a link shortener and was widely used on Twitter. Twitter authorized its own automatic link shortener, but it is nowhere as nice as bitly and lacks the same features. One can still legally use bitly on Twitter because it does not interact with Twitter. Many app developers take the chance and impose their apps onto a site, but when you directly interact and interfere with the operation of a site, you are most likely going to get in trouble.
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