I believe so, although you wouldn't use seeking in an informal conversation. In my opinion it's a bit archaic so I would expect to see it in a book. Hope this helps!

It's a lazy day.

I was lazy today.
Although I had a task to do, I didn't do it.
I listened to music, read books and cleaned my room.
Because it was necessary to the balance of my heart and my spirit

I need to learn the culture and history of the whole world to understand it and grow my spirit

I need more time.
But I'll do it for a long time because my life will be long.

Well done! I'm not brave enough to write a long passage in Japanese. There's so many differences in structure between the two languages, but you did very well :) 

It can be translated as can I, but that word is mostly used for a question one does not expect an answer to; like you are asking yourself a question. So I would translate it as, Maybe I should call you Saliari.. (sorry no greek keyboard where I am!) Saliaris is someone that drools, I don't know if it is of any use to your translation!