At customs, they don't scan the contents of your hard drive(s). They just scan the laptop with x-rays to be sure you're not hiding something else inside it. That is unless of course you were on their criminal list or you were arrested and they decided to deep-search all your belongings.
Anyway, answering the first part of your question, TorBrowserTor Browser is one of your best options. You can download it at https://torproject.org and install it with easy steps. It is essentially a customized Firefox browser, that protects your privacy better, and which uses the torTor network to browse the web. Don't forget to read the really important advice bits written in the download page to ensure you're taking the right steps to protect your privacy.