Experienced developer here. I do Android development on the side (my day job is bouncing back and forth between C# and Python web development). I have some pretty popular apps in the Play Store though.
You will find it's mostly Java, which is still a growing, thriving language, by the way-- despite how many people tell you otherwise. (they usually aren't even programmers and don't know what they're talking about) You will also find that it's generally not a waste of time to learn any language. In this day and age, you should be able to get up to speed with a new language syntax in less than a week if you're an experienced engineer. Past that first week, it's just learning the random language-specific intricacies, so please don't feel like you're wasting your time learning anything. That's never the case. Java is a fine place to start.
Keep in mind that while you'll be working in Java, you'll mostly be learning the Android SDK and the APIs that it extends. Eclipse is probably the most popular IDE, but it's certainly not the only one people use, and you can't only use the SDK with Eclipse, I don't know who said that but that makes absolutely no sense at all. You can use the SDK with Notepad if you want. Google just gives you an easy plugin way to use it with Eclipse.
But you might find that using IntelliJ IDEA (by Jetbrains) to be good as well. My buddy and I started using that last year after a session we had a Google I/O 2012, and we haven't looked back since. It's a phenomenal IDE. It's not quite as extensible as Eclipse, but there are a ton of other features that make up for that. I know quite a few developers that have switched to IntelliJ as well, one in particular who has an app that net him about $700k last year.
Anyway, there's a ton of tutorials and books around. Google offers a lot of assistance too. Mobile development is a cool place to start, I think you will enjoy it. Just keep at it.