Pokemon-go – activate 2 Lucky-Eggs at the same time? If yes, is it working like x4 XP or what

It doesn't sadly. The 0.29.2 (today's release) supports Android Nougat, but as of the current release, it doesn't support split screen.

Don't worry about saving new catch bonuses

Trying to control your catch bonuses during a lucky egg effect is not an optimal use of the XP bonus. You will earn much more rep evolving as many Pokemon as you can instead of catching new ones.

The evolve animation is shorter than the animations for the Pokemon appearing, knocking your pokeballs away or dodging, then shaking until captured. Incense and lures can't get rid of the animation delays, nor are they 100% guaranteed to keep supplying you with new Pokemon as fast as you can catch them.

Instead, you can hold off on using the lucky egg until you have more than enough candies to evolve Pokemon constantly (or as fast as the evolve animation allows you, anyway) for the entire duration of the effect.

As a new player interested in gaining XP optimally, you may also want to take a look at the answers to What's the best strategy for early play in Pokemon-Go?

^{I realized later that OP was the one who asked the best strategy question, but it has relevance for any other readers so I'll leave it in all the same.}