Construct2 comes with an Multiplayer example and there are already 2 tutorials posted from scirra.

other thought: use Canvas. With this, you can just overwrite the canvas with the added ingredient (no need to add new sprites every time). There is a 3rd Party plugin for Canvas.

do you already know how to use "lerp" for the movement itself?

For moving 1 tile on the x-axis, you only have to move the sprite by 32x1 pixels.

Example 1: sprite1.x = sprite1.x+(32)

For moving 2 tiles on the x-axis, you only have to move the sprite by 32x2 pixels.

Example 2: sprite1.x = sprite1.x+(32*2)

quickly installed C2 on a VM Machine, here you can download an example: Link

Update: Also example now attached to the post!

hmm, without a capx (that someone could have a look into it), it is a bit hard to find out what might be wrong.

I am work at the moment, without access to construct, but when I'm back home (unfortunately just in about 8 hours) I can set up an example and share it. Maybe someone else is quicker

is the "score" Variable a global variable? Are you updating the variable on the game layout with the score?

can you do a snapshot of the event you set up? Or maybe upload a capx file? This is much easier for all of us to see where you might have done a mistake.

Put a Textobject on the final layout, read the content of the global variable and paste it into the textobject.

without having a .capx to see that there is no error in your code I just throw a guess and possible situation that your game does not work anymore:

Have you uploaded all of the content from the export folder of your game and not just the index.html?

Maybe you can share a link to your game, this could help us to help you.

Have you read the beginners guide tutorial?

This should give you a lot of knowledge to make such a game you like to do.

A lot of possibilities that you have are there.

My first question is to you, how experienced are you with PHP or Perl?

You could set up a database, put a script on your server and use Ajax to send and receive scores.

If you are not that experienced, you can use other services (facebook, clay.io, ...) that you can implement into your game and save scores into.