1. Americans use -ize mostly, while in BE we use both spellings quite happily and the vast majority can take either in BE.
2. 'First came' implies that there have been other trips since.
3. I was studing here before. It should be 'studying', and I would go for 'have studied here before'.
4- You should look up this word in the dictionary. This is fine. You could also say 'look this word up;, which does sound a bit more natural to me.