There are two different types of install problems happening here. First, the installation of both httpuv and shiny failed with the same symptoms:
This can happen when a previous installation attempt ended unexpectedly, before R had time to clean up some of the intermediate files it creates during installation. Have you tried removing those lock files, as R suggests?
Meanwhile, the second error:
This indicates that after package installation had begun, something went wrong with R's internet connection (if this has happened before, it could be the reason you have those intermediate files hanging around). This isn't easy to debug from afar — it most likely has to do with the reliability of your local network or its connection to the internet.
Overall, though, is there a reason you are still running R 3.3? (that version is from 2 years ago — the current version is 3.5.1) Updating R to the latest version will mean that many more packages have available binaries, easing your installation process considerably.