Remove only salt from salt water
You could remove the bulk of the sodium chloride (and most other salts) by evaporation and crystallization. Most of the impurities you are looking for are going to stay in solution or suspension when you filter off the salts.

You could also use dialysis to remove the remaining salts: this requires a bag or length of thin-walled tubing made of a common polymer such as cellulose acetate. Tie off one end (the bottom), put the concentrate from the above step into the tubing, and tie off the top end. Then place it in a bucket of distilled water. The salts and other small molecules will diffuse out into the water, whereas the higher molecular weight materials like toxins will stay in the bag. You may need to change the water in the bucket a few times to get rid of all the salts.

You will still need some chemistry to figure out what substances remain in the bag. With seawater, it could be a very complex mix. However, looking at it with a fluorescent light might show something interesting. Good luck, and hope you get inspired to study chemistry!