>Is there a way how I can copy blocks of code outside the vim window to another application without also copying the line numbers?

    set clipboard=unnamed

On Windows at least, that will make Vim use the system clipboard as its default register (the one you yank or paste from when you don't explicitly specify a register). Alternatively, you can yank and paste from the system clipboard like you would from any other register:

    "*y<movement>
    "*p