Stellar

The game idea is an interesting twist on a matching game.  Can't say I care for it myself, but I can see the appeal.  There are a few areas that definitely need cleaned up, however:

First, your tutorial needs to be a separate item on the menu.  A returning player needing to hit "no" every time they want to do arcade is an unnecessary hindrance to gameplay. I would rename it "How to Play" as well, to keep it a bit more casual.

In the tutorial, your text does not overlay everything as it should.  A star or meteor in the wrong place completely covers up text.  In addition, you have misjudged how long it takes to read certain blocks of text; a better solution would be a tap icon with "tap to continue" functionality. Also, is there no way to exit the tutorial?  Had to restart the game to get back to the main menu.

As far as the meteors go, an insta-death mechanic is unimaginative and feels unfair at times.  A better solution would be to have something like the asteroids unlinking any star chain they run into, so they are actually an obstacle to the player's high score instead of an arbitrary loss mechanic.

Speaking of round time, the clear beginning and end of each round needs to have more thought put into it.  A number of "lives" doesn't make sense and feels tacked-on to what is essentially a matching game.  I can't offer any real solutions as this genre is outside my experience, but this does need reevaluated.

As far as technical concerns go, a single click can perform multiple actions, with a single click linking two stars and killing a meteor if the positioning's right.  You need to give everything a z-order and only interact with the top-most uninteracted item.

All-in-all, your basic mechanic is interesting, you just need more thought into the presentation and secondary mechanics surrounding it.  Sorry I can't offer more solutions, but hopefully this gives you a list of things to think about.