mount.nfs 192.168.1.106:/home/mydir /mnt/tom
What are the permissions of the mydir and tom dirrectories? Do the two computers use the same UIDs for the same user?
Your hosts files have the names in the IPv6 entries for localhost. I don't know if this is proper.
127.0.0.1 localhost.localdomain localhost localhost4
:1 tomcat.faygrase.com eagle localhost6.localdomain6 localhost6
This entry is for tomcat, but has name entry for eagle. That is how one blocks websites using the hosts file.
You have 2 enties with fsid=0 in /etc/exports. Only one should be nfs-root.
You should bind mount the directories to export over directories which are subdirectories of the nfs-root directory.
E.G. /srv/nfs/mydir and /srv/nfs/mydir1. Then /srv/nfs/ will be the nfs-root with the fsid=0 entry in /etc/exports.
On the client, the fstab entries will look like
tomcat:mydir /mnt/mydir nfs
tomcat:mydir1 /mnt/mydir1 nfs
Notice how the nfsroot part isn't included, so you just use hostname:share instead of tomcat:/srv/nfs/tomcat.
You can use options such as nosuid,noexec,ro on the bind mount options that aren't present for the from directory. Bind mounts allow you to also share a subdirectory with freer permissions without needing to grant others rx permissions to your HOME directory.
There is a root_squash and an all_squash option. I don't think there is an all_root_squash option.
Check the logs after a mount attempt fails.