There are no definitive answers to your questions since the answers will depend on the preferences and opinions of those answering your questions.
The answers also depend on what kind of web design you have in mind. You mentioned WordPress, and people do design websites within WordPress, but those designs are limited to the capabilities of WordPress and whatever WordPress theme is being used. Going deeper than that requires knowledge of how to work directly with the underlying template code.
It’s also possible to design websites using online tools that require no (or very little knowledge) of any coding, but doing it this way will limit you to whatever those online tools allow and are capable of doing.
Website design has gotten so complicated that most people involved with it specialize in a particular aspect of it. For example, there are people who specialize in just the interface and who mostly hand off their mockups to others who specialize in the front-end coding and who, in turn, hand off their coded front ends to the back-end developers who write the scripts that glue all the pieces together and connect it to the database holding the structured information. That process could be broken down even further into people who specialize in user experience design or framework development or specific scripting languages or content management systems.
Personally, my favorite web design tool is a code editor and a browser, but not too many people would give you that answer. It really does depend on what you want to do and where your aptitudes lie.
Then again, maybe your interests are limited to just designing the user interfaces and working with someone else who handles the majority of the coding. If so, some of the most popular tools used to design interfaces are Sketch, Figma, Zeplin, Adobe XD, InVision and even good old Photoshop, among others. What tools are best really depends on the situation and whether you’re working alone or within a team.
You have shared detailed information with me regarding Web Design. I am familiar with code editor tool, but i personally never use it. As my coupon website CouponGot-com is designed with a ready-made Clipper theme. So i need some advance web designing skills to do customization in current theme. I will also have a look on all these tools like ketch, Figma, Zeplin, Adobe XD, InVision, old Photoshop.