touch: cannot touch `/usr/share/tomcat7/logs/catalina.out': No such file or directory

When installed using the tomcat7 package, it is intended that you start and stop Tomcat using upstart (service tomcat start) or the /etc/init.d/tomcat script. If you start it using the startup.sh script then it is likely to have its environmental variables incorrectly configured.

Please see my answer to your previous question (How should I install Apache Tomcat 7 for use with Eclipse?) for a better way to install Tomcat if you don't want to run it as a service.

just create the missing folder like this:

sudo mkdir /var/tomcat/logs

then run tomcat again like this:

sudo sh /opt/apache-tomcat-{version}/bin/startup.sh

The message itself is self explanatory, if you don't know the hierarchy of the Unix/Linux File System, and how it works, i highly recommend you to start watching some tutorials.