Storing (Days) in database

You don't store the day. Just use a datetime type, use the dates array in your model and use Carbon to format the date,

I would create a new migration with timestamps as Laravel cast these to Carbon and you can do a lot in the output.

public function up()
    {
        Schema::create('listing_working_hours', function (Blueprint $table) {
            $table->increments('id');
            $table->listing_id('listing_id'); //I would stick with only the id and delete this one
            $table->timestamp('from');
            $table->timestamp('to');
            $table->timestamps();
        });
    }

so when you create a a new data in that table you would have all the dates you need in full format.

Then in your model -

    /**
     * The attributes that should be mutated to dates.
     *
     * @var array
     */
    protected $dates = [
        'from',
        'to',
        'created_at',
        'updated_at'
    ];

If by 'Friday' you mean any friday then store an integer for the day of the week, ie 5

You could perhaps lean on Carbon constants but probably not necessary

https://carbon.nesbot.com/docs/#api-constants