How can I move items horizontally in Terraria?

All "Items" that lay around like dropped gold coins respond only to gravity. The only way to move them is by creating wired wall on the ground and deactivate them, so the item will fall.

I don't know of any way to move or push items in an other direction than down.

You can't move items automatically, but you can move yourself to the items automatically. If you set up a minecart track, using bumpers at the end, you can hold one key and move along the minecart track. Some autoclickers are able to hold a key for you.

You can then use minions or lava across the ground to kill the mobs, or a weapon with an autoclicker.

If you don't trust an autoclicker, you can use an autoswing weapon and sticky tape down your left mouse button; in controls you can assign right click to a movement key and tape it down too and that will keep your character moving.