sotak, first of all, I would put most of the code in the collision section in a function so you don't have to duplicate the code so many times...
Also, you have several problems with webstorage. You are saving the text "Score" instead of the value of the Score variable, and you don't need to do that every time the score changes. Webstorage is for saving data when you close the game after you are done playing. Then the next time you open the game you can load the data back in (to keep a local all time high score for example). But you are resetting the webstorage "Highscore" field at the start of the game, in event 2, which would wide out the previous high score (if it was being correctly saved). And, on top of that, there are a couple places (events 3 and 7) where you do not have Highscore in quotes - so Construct2 will use the value of the Highscore global variable of zero, rather than the text key "Highscore".
Now, for the main problem you asked about at the end of the game, it looks like you are setting the Highscore text object to be visible, but I don't see any place where you give it a value.
So, the main thing to keep straight in your head is that you have three completely separate things here: 1) the global variable Highscore that keeps track of the highest score achieved by the play while the game is running. 2) the Highscore text object that can be used to show that high score to the player on the screen. And 3) the Webstorage "Highscore" field that can permanently save the high score on the players computer hard drive when they quit the game.
The main flow should go something like this: Load in Highscore from Webstorage if it exists, otherwise create it and set it to zero. Set score to zero. Play game. You have the right idea in event 7, where you add 1 to Score. (but you can take out the Webstorage line there)
Then when the game ends you want to check if Score > Highscore, then set Highscore = Score, and save it to webstorage. Then set the text object Highscore to something like "Your score="&Score&", High Score="&Highscore... then button to restart the game...