Yes, but more people understand 'programmer' than 'coder'. I've told somebody I was a coder, and they thought I worked for the CIA.
No, that would be a decoder, which is a skill one must often learn to solve some puzzle caches.
I've never heard the term "coder" to refer to someone that creates web pages. I've seen it used in the context of a larger software development enterprise that has the luxury of separating software design/architecture with actual programming. Once the requirements for a program/application are defined a systems analyst/architect/designer might construct the algorithm and business logic necessary and even go as far as providing pseudo code for an implementation and then "coders" would write the actual code (program). In practice, those roles are often not separate.
As I wrote earlier, although the syntax for a web pages is a markup language it is not uncommon at all for that markup to be produced using a programming language.
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