I used latches that you just had to push down to open the cupboard door, you can also use them in drawers. They worked so well. I got them at Baby Bunting.
Yep that. We've used those on most of our cupboards, but got ours from bunnings. Bit fiddley at first but you get used to it. And gated off hallway to laundry/toilet. Also have gate on his door, but that's to keep the cats out.

Have an old fashion bolt lock on pantry, but again already had that set up to keep the cats out. Also have a plastic swivel lock on fridge, but haven't used it yet as its too hard for him to open.

My DS is a bit full on, and if we didn't have them set up he'd be constantly going into them. I think he just tries to mimik us. That being said I have set up a drawer on the kitchen with some utensils and bowls etc to entertain him. My SIL kids got into pantry and poured a heap of its contents on the floor so I'm a bit weary.