Alone?! NO!!!! Why on earth would you think that would be OK?
Monkeys (even small ones like Marmosets and Tamarins) are troop (family) animals. If they are left alone, over time they will actually become neurotic. Yes- CRAZY! They will pace back and forth for hours at a time, scratch until their hair falls out, and even chew on their own limbs! Not to mention, monkeys kept single will be 100% more aggressive towards their owners. Trust me, I've worked with marmosets, tamarins, squirrel monkeys, spider monkeys, capuchins, lemurs, macaques, vervets, and more. I am an owner of 2 Capuchins. I've seen many owners purchase just 1 monkey and think their human companionship will be enough to satisfy it. Sadly, those same monkeys are ALWAYS the ones that end up in sanctuaries.
Why would you even ask if it can imitate human actions? Of course it can. It's a monkey. They all do. If you leave it alone everyday with no supervision, I guarentee it will be dead within a month, if not sooner. They all will chew on walls/crown molding/doors/furniture so if you have lid paint or any toxic stains on them, it could kill them. Also, they will chew on wires to lamps, computers, TVs, etc. You know what happens with electricity. They will even shred up dish towels, wash clothes, small fabrics and eat them. I know of a monkey who recently died because of that. And turning on gas... yes. My monkeys would have that done in 5 seconds. A marmoset, probably would not learn that trick as quick. But, give it a couple weeks/months and it could.
I have nothing against owning exotics. Like I said, I have 2 Capuchins. But, I don't encourage someone to get them when they are not prepared. Firstly, I'm guessing since you have an apartment you don't have an outdoor habitat... Yeah, that right there is terrible. I'm not even sure animal control would allow that. Most communities, sub-divisions, townhouses, and apartments actually ban monkeys. If it's confiscated from you it could face being euthanized. Make sure it's legal in your apartment. The minimum cage size requirement for a Marmoset is like 5x5x5 feet I think. Can you put that in your apartment? In all honesty, you should consider moving some where that you can have land. (Even if it's only half an acre!) An outdoor habitat is so important. You do know that without UV light they will die, right? So, if they are in the house (which I don't encourage) they will need a UV lamp.
If you really want to get, please be educated. The majority of exotics die within the first 2 years because their owners do not know how to care for them. Do you know what they eat? Or how they act during heat and sexual maturity? You will need to know all about their care, diet, housing, enrichment, behavior, and husbandry. If you need any help regarding information on how to care for them, feel free to email me. Again, I have nothing against you owning one. You might would make a great owner! But, it's important to be educated first. Exotic animals owners have such a bad rep as it is, let's not give the public anymore reason to fuss at us! Monkus83@yahoo.com