does this game have annoying time/day limits?
Not like other games.
Time passes while you walk, and some characters appear only at certain times. Provided you don't change the current location, time will pass but it won't switch between the three states (Day, Evening, Night). You can even repeat scenes indefinitely so you won't get the usual "I've already done this" message you get in other games. And you can also get an item from the store that lets you set the time with no penalty or passing the day.
What
is annoying is the stamina mechanic which starts very small but grows bigger as you play. Also money is a bit slow to come by. You can solve both of these issues if you use the save cheat I included above. There are items that give you stamina that you can stock, but you can also increase it to a ridiculous amount so that it's not an issue. If you do this you should still sleep sometimes for the scenes and also because the bus lady only reappears after you sleep (for the first 3 times, until you unlock her first scene).
The three cats quest is the only thing that time makes kinda annoying but people have already posted their locations and time they appear in comments if you don't want to bother searching.
Also, you can always find the sister characters but they spawn on different locations according to the time, both in the house and in other locations outside. Each location they spawn at has different scenes for the character.
tldr: Yes, but it's not annoying. The annoying thing is the stamina that you can cheat away.