We just used 2x4 scraps screwed to the studs in the corner for counter support. Go ahead and use a 2x4 rather than an 1x2, it'll only cost a few more cents, and if you ever need to stand on the counter it will support your weight better.

We didn't do anything in between the drawers, no clearance was required. Everything worked perfectly.

I have 3" fillers in both corners so the hardware clears the adjacent cabinets.

This photo shows the peninsula sink base/blind corner going almost to the wall. I have 12" cabinets on the back of the peninsula and they have a top (the little bit of cherry you can see in the left corner). We have quartz on all the cabinets.

3" fillers on both sides of the corner is standard. I did 4" where I needed drawers to clear our oven handle.

My cabinets were custom built.

As you can see in the picture, (PLEASE ignore the mess, I'm in the middle of cleaning the kitchen and stopped to snap this photo) my dishwasher is on the other side so I needed clearance for the drawers to be able to open.

My cab maker just built the box bigger on that side to allow for clearance, then built a piece which goes down the side of the dishwasher, over the top of it and attaches to the sink cabinet.

He brought strips, 1x2 I think, that he mounted to the wall on the studs for the countertops to rest on.

My counters are granite and the 1x2 supports it just fine.

Drawer thickness, hdw, i/2 suans, full susans and opposing appliance are all design stage considerations.

While minimum cleating with 1x4 or 2x is needed in custom cabinetry, it and fillers are far more prevalent in bag-n-box cabinetry.

Thank you, thank you.
We will be using IKEA cabs...waiting to see more of the US Sektion to make a final decision.
We will DIY the whole thing.

I was figuring 3". I am hoping to center my range so appliance handles shouldn't be an issue.

I just measured - it's 2-1/2 inches from the edge of the drawer to the adjacent cabinet. My cabinets were custom, and my cabinet maker had the benefit of having my hardware before he started cutting lumber, so he could minimize the filler while ensuring clearance.

Scrap 2x4's support the countertop in my dead corner.

Cabinet hardware before assembly is a good idea too. :)