I can advice vista app https://create.vista.com/colors/color-na...dger-blue/ it's free editor optimised for web use. Personally I've never used it especially for headers. But I use templates there for creating banners for people and it fits good for it. I think you can do some headers there for easy, it have a lot of free templates and fonts for all kind of work.
Depends on what you mean, if you mean software obviously Photoshop is the way to go as the industry standard software. In terms of social media headers, your best bet would probably be twitter headers in my experience. The headers are large enough for great designs and there are a lot of people looking to create their own brand identity throughout their social media channels.