You can have double cabinet stacked all the way to ceiling just like built-in wardrobe cabinet.

How close is close. I don't think anyone put fridge next to hobs anyway. The air flow in kitchen is more on the efficiency factor. The hood is circulating or blow out. If blow out, the heat will not accumulate in kitchen.

I think melamine has different grade also. The inner core is wood particle. While the surface is robust and water resistant, the cut side can still absorb water and expanded. Even after wiping the dishes it is still damp. Putting in closed cabinet is not the way in hot and humid climate like Malaysia. Even if your whole house is air-conditioned, there is still no air flow in cabinet. Over time you will get clumsy and water may dripped, go to the cabinet cornet and absorbed by the melamine.

I have less used cooking utensil and dishes in rack under my cooking hob (to get heat and blower from hob to do the job ) but part of the door has perforated stainless steel sheet to help with ventilation. The door under sink cabinet is also the same. The sink can be cold and form condensation underneath inside the cabinet below. Having perforated door will help dry the cabinet and prevent stale smell or become roaches heaven.

My table top has plenty space. So, I put on top at a corner just a bit away from sink. If you need to have your dishes inside top cabinet, make sure you have perforated door to prevent trapped humidity.

Sure. No stale smell and no roaches because the hole is small around 3mm only. I used stainless metal sheet which I think easy to find in market. Not using the metal net because it will not look good and fragile also. I just made it as strip, not whole door which I think more stylish. Something like my drawing below.