The major problem with living in a surface dome will be radiation. Mars radiation is too high for constant exposure. People will spend most of their time under radiation shelter.
A tall thin dome won't provide much radiation protection. Although one that generated a powerful magnetic field of its own would provide some. More likely the dome would begin as a cluster of small, domes covered in dirt for shielding. Later as the colony grew some of the intention domes could be linked together to provide support for larger domes, and so on. Eventually, fairly thick leaded glass could be used although this would be a very heavy and substantial structure, like a vast stack of old school CRT screens.
The dome would only be able to show light part of the year. In winter CO2 and water ice would form on it unless it was highly heated (just as they do on Earth.) Worse, the martian dust, especially in the month long stand storms, would coat it over. A big dome of glass or plastic, even grounded, would be one hell of static electricity generator.
Power would have to be nuclear. Solar would be weight/watt cost prohibitive and would suffer the same problems with dust, ice and storms that forced the Pathfinder robots to hibernate for months at a time.
Primary oxygen will come from algae tanks with food plants providing oxygen in the carbon cycle. Algae will be part of waste recycling as well.
The problem with domes is that while they are very efficient enclosures of volume, they are poor encloses of area. If you look at images of interiors of large existing domes, you see small areas with vast amounts of open air above them. On Mars all that air is generated, filtered, heated and pressurized. To make efficient use of the space, you would have to fill it with large tall buildings, and then you've lost your open spaces.
A better and bigger dome could be produced underground using a nuclear charge technique, experimented with back in the 60's. An underground nuke in relatively soft rock compresses the rock and melts it, followed by an injection of water into the center of the molten mass which expands and presses the melted material into a dense glass, then a type of cement is injected. Soviets used that to build big chambers for storing oil. After it cooled, a coating of plastic sealant makes it airtight. Radiation is minimal, actually less than surface construction on Mars, don't have to worry about heating the air, external radiation or sandstorms or efficient use of space. Plus, the materials you need to ship to mars are much lighter.
The population density of the dome is really dependent on how dense you want to pack them in. The energy production and rest of the physical plant will be outside the dome as will the agricultural. Plants don't need a vista and plants will have to grown under false light on mars anyway. As always, energy is your final limitation. With enough energy, you can do anything.
Having spent a summer knocking around in a hazmat suit directing aerial spraying, I kind of doubt people on Mars will be big fans of wide open spaces. The nicest spring day pales when view through a face plate and filtered air. A 3 billion year unchanging landscape will get old in a hurry. Most likely a deep, secure efficient underground facility with some nice projections of Earth on the walls and ceilings might go over better.
I would suggest looking at the population densities of contemporary Tokyo, one of the highest in the world, to get a feel for how many you could cram in.
