Building the infrastructure / superstructure shouldn't be all that hard even with today's technology. Look at the capacity of something like a modern skyscraper or airliner or ship.
One could build anything from personal sized to "small city sized" ships with the usual plastic, aluminium, titanium, fiberglass, epoxy, glass, steel, carbon fiber, et. al. materials.
The thing really missing for space exploration are good drive systems to allow any significant mass to be accelerated significantly, especially over long durations. Journeys even within the near solar system are usually done with the most energy efficient possible orbital transfers and still they can take months for the journey even between points of closest approach, and that is with relatively small payloads like robot probes / satellites. Yet they use some fairly large rockets just to accomplish that feat.
To send something like a manned laboratory or habitat cargo to Mars would require something more than an order of magnitude better than we have today and that's even for the "slow boat" trip. Even if you build everything out of aluminium, titanium, carbon fiber, et. al. you're probably still having to transport significantly more (order of magnitude?) payload size and mass than a normal space probe or orbiter would require. Then add on water, fuel for a return trip, et. al. and you have a problem of fuel / thrust / drive moreso than an issue of constructing a durable light weight habitat.
The main problems for the superstructure / infrastructure / system engineering of the overall structures, though, would be:
a) making ones that are actually air tight and don't leak too much over time.
b) making ones that are insulating enough not to leak too much heat out.
c) making closed ecologies to recycle air, water, soil, waste, et. al.
d) radiation and micrometeorite shielding of external threats
e) shielding against one's own drive / power systems if necessary
f) reliability and maintenance of all critical systems
g) being able to do significant construction projects from individual pieces away from earth since the overall units would be too big / heavy to lift from the ground, so we'd have to assemble them in orbit, on the moon, on Mars, whatever.
h) solving human factors like claustrophobia, exercise, boredom, human error, et. al.
That's probably all relatively doable relative to the propulsion / energy systems problems for which there are few attractively obvious solutions even for rapid / extended / high mass travel around our own solar system. One starts to need megawatts or gigawatts of power for lighting, environmental issues like heating / water purification, motion / thrust, engineering / factory / industrial / chemical needs, heating, et. al. and one starts to find one doesn't have fuel mass / space, or one doesn't have reactor technology to efficiently use the avaialble fuels, or whatever.
I don't see how using asteroids will really help, they weigh a lot and don't really give you much advantages in habitat / energy / space / whatever that you wouldn't already have in a manmade structure. I suppose you could do something like drive a comet around if you could use some of the light materials in it for reaction mass or energy generation or something but even so you'd be first needing energy technologies we don't have today.