In general, yes, you can take your time exploring, and it is often better to put off doing main plot quests until you have explored and done the side quests for the area.
If you accept a quest in Verdistis involving arson, you must do so that game day.
If you leave Aleroth at the start of the game without completing some or all of the quests there, forgetting about them and doing any of the main plot quests that give you an invitation to the castle will result in them completing without your help (so lost XP and other rewards).
In the Dark Forest you can do something with a bad result; undoing it will give experience, failing to undo it will eventually have a negative effect on some side quests in the Dark Forest. minor spoiler:
You can release something trapped, who will tell (and show) you that they can not be killed.
