I looked it up to see what …
This is redundant. Twice.
"looked" and "see" have the same meaning, and the "it" and the "what" each refer to the same thing.
Any of these would be better:
- I looked up what … .
- I wondered what living in a castle would be like, so I looked it up.
- I wondered what living in a castle would be like, so I looked it up at the library.
… what it feels like to live in a castle.
That's okay if you want to live in a modern castle today.
But it's more likely you were thinking of castles as they were centuries ago.
If so, either of these would be more appropriate:
- … what it felt like to live in a castle.
- … what it would have felt like to live in a castle.
It seems like living in it is more uncomfortable than I thought.
Here it doesn't have a proper antecedent.
The first sentence says "a castle, so there isn't any specific castle for it to refer to.
It would be better to use "one", which in effect selects an arbitrary single instance of "a castle".
- It seems like living in one is more uncomfortable than I thought.
But again this is okay when the preceding sentence uses "feels".
But if you use "felt", then it would be better as any of:
- It seems like living in one was more uncomfortable than I thought. People would sleep in beds that … .
- It seems like living in one would be more uncomfortable than I thought. I would have to sleep in a bed that … .
- It seems like living in one would be more uncomfortable than I thought. I would have had to sleep in a bed that … .
Firstly, castles aren't designed for dwelling purposes — they are fortresses to fend off enemies.
Again, a past tense would be more appropriate:
- Firstly, castles weren't designed for dwelling purposes — they were fortresses to fend off enemies.
The key thing to keep in mind is to preserve a consistent tense and point of view throughout the entire essay.