when i search the web on a laptop, can a third party view without my knowledge?

Answer 1

All search queries through a search engine etc are saved for future reference. A log file contains your IP address, machine name and what you searched on.
For example, you use multimap to find a locations, this is stored on there server and in future this infomation can be retreived.
If you don't want somebody to know what you are searching on don't search. But if what you are doing is above board and legal you should not worry.

Answer 2

When you search on anything, a third party can view your search queries if your computer has spyware, adware, freeware, etc.

So yes : ]

Answer 3

yes