Yes. Beyond food and supplies, people would have to either want to spend their lives while on Mars in containerization or there would have to be a large pressurized common area for work and socialization. With a thin atmosphere stuff falling from space is a problem as it would be on the Moon so building underground would be required. That's why I think going to Venus first makes sense, get people used to the long travel periods living in confined spaces dependent on machines.

A spacecraft could double as living space on the planet, alongside whatever other prefab buildings they bring along. A cargo hold packed full of prefab walls could itself double as building space, once emptied. Also there would be more opportunities to leave those spaces to go outside.

It would certainly still be cramped by conventional standards, but conceivably much less so than the flight there.

Yes. Mars has an extremely thin atmosphere that would kill us if we did not have pressurized suits and stations.

Don't forget the radiations. The main problem of the Mars atmosphere is that it's too thin to stop enough of them for human beings.

They'd be getting out of the habitat regularly to do science/construction, though.

You can build more space from local materials.

Also excursions, though you need a space suit.