They’re adding another length of rod to go deeper. The brown liquid that sprays out isn’t oil, it’s drill mud which is literally just premixed mud which is added to the hole to help stabilize the sidewalls and also cool off the bit.
The big mechanical brace they move around is used to hold the active rod in place while spinning a different rod in or out.
The brace built into the floor around the active rod hangs the whole drill column in place while extracting, which can weigh tens of thousands of pounds suspended over a hole that can be thousands of feet deep.
The chain is used to create friction and tension on the rod to pull it into place horizontally when trying to slot the next length of rod. In some cases it also provides extra tension when tightening the rod connection.
The stuff he brushes the threads with is pipe thread grease to help disconnect the rods after inducing incredible pressure on them from drilling.