Ruby, DJango, etc... won't last because they are nerdy designer languages to make people feel special and sell books. I would recommend .NET, PHP, or Java.
.NET is more used in corporate dev (because there are license fees). PHP is used by small business. Lots of PHP jobs in big and small business and it's been around for a long time.
Trust me, languages come and go and some are forever. Javascript, PHP, SQL, etc... will be around so they are a good foundation for any web developer.
For databases, just learn SQL. Then if you have a specific problem, find the cache or database that solve it. Most of the time poor coding is the issue and not the database.
API's are used a lot, but there's not much to learn. Most of them have abstractions that are very easy to use with a reference document.
You only need to learn one JS framework. If you know Javascript then you aren't really learning much of anything honestly. There's a ton of them so just choose whatever is most popular or is required for the job. If you are a freelance developer, then get good at one and use it for everything.
Javascript (or some form of it) is used in a lot of other things... Photoshop, After Effects, etc... use them for advanced stuff. If you only learn one language, I would recommend Javascript.
Also, don't code by hand. Get a freggin' IDE. Anyone who is proud that they wrote something by hand is a moron.
Don't fall for the object oriented BS. Good coding is a mix of procedural and global definitions, as well as object definitions. Most programmers would disagree but they can't give a valid reason why objects are better. They have their purpose and you should learn to use them correctly.
They missed Photoshop on the design side. It's pretty much the standard for mockups and designs. If you create logos, use illustrator. Always save in .png, unless it is a photo or you have a valid reason to do otherwise.
Spritemapping, and DNS strategies will reduce load time. Bad database programming is usually why a website loads really slow or crashes. Usually well coded SQL is as fast as most of these other replacement databases. However, if you are writing something like a search engine or something complex, you might consider choosing something else.
If you are just starting out, just learn MySQL or MSSQL (basically the same).
Just my opinion but I chose PHP, MySQL, Javascript, HTML, and CSS about 15 years ago (or 20 years? I dunno) and they are still used everywhere. They are living languages so expect continued education for as long as you are a developer. Frameworks change but abstraction and organization is the purpose of them so just be aware of good coding practices and choose what makes the most sense to you.
I've had many programmers and developers try to convince me to change my mind, and then 5 years later they come back and try to convince me of something else. In the end, they just end up on the same page as me. It's easy to get caught up in the pop-culture and waste time learning shit that disappears after a while.
Oh yeah, all programmers smoke pot.