My answer would be equivalent to me Googling that question for you. Do you have any questions about what results you get from using the search term ‘2D game engine’?
I do not know what your current skill set and/or expertise is, but for front-end web development you need to know HTML, CSS and JS. A very good understanding of those 3 plus a framework like Phaser, already mentioned by @DavidMatthewFraser, would be a good starting point for making web-based or browser games.
Game development in general is something else entirely. What platform do you have in mind? Desktop, laptop, smartphones? What OS? Windows, Mac OS X, linux or all of them? You’ll be probably looking at Java for smartphones and C++ or C# for the rest.
Sorry, but I can’t help you there. I am not into game development, I don’t even play games.
Are you just starting with development? If so, stick to one thing at the time.
Spend a couple of months with HTML, CSS and Bootstrap. After that study half a year Javascript and then some JS frameworks. That is just the front end. If you want to become full-stack like your bio mentions: you will probably need another 6-12 months for the back-end.
Adding to the existent advice, you could look for requirements in the existing jobs postings.
For the little that I know from this market, Unity and Unreal engine seems to be the most popular frameworks for game development. Unity allows you to develop using C# and Javascript while Unreal Engine uses C++.
I am not sure, but I think that for IOS devices there is a native solution offered by Apple.