Oven – Purpose of hole in stove leading to oven

Yes.

It's much more fun to cook with gas, and the way I see it, any incentive I can provide for myself to cook good food at home is a major net positive in quality of life.

The setup I have is three gas burners and one electric stove top element, and an electric oven. The electric stove top really comes in handy when reducing stocks or making long-cooking soups and stews, and it can significantly reduce the amount of gas you use in cooking.

For oven I would definitely go electric. See the When baking is it better to use a gas or electric oven question.

I have one 5 kg liquid gas bottle stashed under the sink, and it lasts 3-4 months of heavy daily cooking for two, maybe 6 months in the summer when I eat more salads etc. In addition I have another 2kg bottle for backup if I run out of gas in the middle of cooking, and for the day or so it takes me to haul another bottle from the store. Having a smaller backup bottle doesn't waste too much space.

I've been considering upgrading to a 11kg composite bottle, which I expect to last 10 months to a year, and it's way more economical. So far though the convenience of having a smaller bottle I can carry to the store for changing without a sweat has been great.

The burners on essentially all electric stoves are binary in that they are either fully on, or fully off. It would be more expensive and less energy efficient to use electronics that continuously vary the current flow through an electric element, and this would make no significant difference in temperature behavior at the cooking surface. Instead, electric stoves use a bimetallic switch which is a relatively simple way to have an on-off pattern with variable on/off times. To create constant heat, all electric stoves use materials that are bad conductors of heat between the electric element and the cookware surface to buffer the huge temperature swings at the element and produce very steady heat at the cooking surface.

The difference you are seeing between electric coil heating elements and glass-ceramic cooktops is that in the electric coils there is an inner heating element, then a thick ceramic layer, followed by an outer layer of metal. The element itself is heated in a binary manner, but all you can observe is the heat after the buffering of the ceramic layer has made up for the large fluctuations at the element (i.e. the outer metal glowing fairly constantly once it's heated). In a glass-ceramic cooktop, since the buffer layer (the glass-ceramic surface) is translucent, you are seeing the actual element glow (often this is an infrared lamp instead of a resistive wire) so you are viewing the non-buffered heating pattern. If you had a clear coil, you'd see the same heating on/off patterns in a coil stove as you do in glass-ceramic.

Consequently, if you measure the surface temperature of a glass ceramic cooktop, you should see a fairly constant temperature.