Is there any kind of timelimit, when you didn't take any quests?
Hmm. Not exactly time limit. You can miss one NPC if you bump into her on Marston and not beat and enslave her right then and there. She won't be there if you leave the map and come back later. So it's a one time only chance that appears after 30 days or so.
You can miss the stormchild simply by visting the slave market on a stormy day and not buying her, again, she won't be there the next time.
Several seemingly generic NPC raiders/bandits are actually unique ones so capture anyone you can. You will definitely miss Cassius if you don't capture him. If you are experienced player, this won't be an issue but if you are new or relatively new you definitely want Cassius in your party.
If you skip an end-day event to enslave an intruder, you will never get Kelly who comes with Crackshot and very good with science.
If you do anything about female urchins stealing your food constantly you will miss out on an npc. You have to let them steal, that is, ignore the report on them untill one seeks you out.
An advice. Try not to focus on a single character too hard or too long early on and focus on building up a strong fighting force of 4 followers because when the Terror pops up, you need to deal with it fast or else the Skyguard takes it out and you miss out a bonus. But it's a real beast and you will need a heavy hitting force in DuraPlate to have a chance. So balance between eco-houseupgrade-your'A'team. It's not actually hard because eco=fighting. Point is, don't neglect fighting.
You won't be one-shotting bosses, the game in this regard is more akin to MMO's. With a fully built and geared up team you just make it kinda easy if you bring 4 followers. You won't win alone.
Yes, the game takes years easily so that's not abnormal here. You WILL leave the city because some quests will take you out of it. There are no random encounters so it's not like you will be slaughtered if you step outside. You pick the fights. 1 exception exist, the game tells you about it.
Do NOT try to push the Prowler quest to it's completion early. The difficulty of the end fight is quite daunting compared to what you will be used to before it.
Don't worry, Aria 30 days just means you can't by her for 30 days. You can leave her there forever if you want.
The only real time limit beside the mandatory instant capture of aformentioned NPC at Marston is Dakota's birthday. Once you upgraded Amiee's shop and rescue Dakota, she will invite you to her birthday. That is of course time limited. Be there on her birthday. The journal will count it for you.
Another one which is easy to miss.. is an endgame NPC, you will only meet her after you install the 3rd Republic. One npc ask you for money and then leaves. The journal will tell that she is off to secure a deal. But that will change into "You have X days to find her or she'll be gone". If you miss this change in the journal, she'll be gone. You will have 15 days once the journal entry changes. It won't warn you about the change. You will have to notice it yourself that the entry changed.