Small portable grill for a studio flat?

If you have access to a well ventilated area and don't mind using charcoal, shichirin are my absolute favorite style of small grills. They also come in various shapes and sizes. You really should use them outside, though, since they release carbon monoxide and their temperatures of 1200°C+ can create a lot of smoke if you are grilling something fatty.

In my experience, small electric grills don't really get hot enough to do anything useful culinarily that a regular range/cooktop couldn't do.

If you must use gas, you could try getting a propane or natural gas camping stove, some of which come with grills.

It won't be as powerful, but there are also some small grills on the market (also see this one) that work off of convenient butane canisters.

Finally, if you already have a gas stove, there is a type of handheld grill that is popular in Japan. It has a metal grill grate on top of a ceramic diffuser. It looks like this:

The ceramic diffuser is the white part below. You hold it over your gas stove and the ceramic evenly distributes the heat across the grill grate. Unfortunately I don't remember what these things are named. Does anyone know?

Yes, there are such grills. Usually created by companies which make low-end kitchen equipment, so don't expect wonders of them. On the other hand, I've owned (and still own) several kitchen devices made by such companies. They are somewhat frail and underpowered, but do their job, and offer a good value for the money.

If you are in Europe, take a look at Severin products. I don't know if they are available in America.

This is an example from Amazon.de. The grilling area is 37x23 cm, slightly bigger than an A4 sheet of paper.