Remember path to installer's temp cache directory, which is printed right after executing "fenics-install.sh". For example:
user@host:~$ bash fenics-install.sh
Created temporary directory /tmp/fenics-install.aauJa7 for FEniCS installation.
When the installer will ask user input to select build type, open cache directory in file explorer and search for file named "suitesparse.yaml". When you will open it in a text editor, it will contain a link to http://www.cise.ufl.edu/research/sparse/SuiteSparse/SuiteSparse-4.0.2.tar.gz
Replace that link with a working download link(you will have to google for it) for example,
http://faculty.cse.tamu.edu/davis/SuiteSparse/SuiteSparse-4.0.2.tar.gz
save that file and continue script by choosing build type.
Do same for other urllib errors.