I'm running on a restricted machine space/memory where I have to remove all un-needed modules.
Is it considered safe to uninstall core optional unused modules?.
modules like: Book, Forum, etc.
Yes it's safe to remove them. But I would recommend you not doing so. These modules are just tiny modules and it won't give more than 1 MB of space to your system.
However, if you are no longer using a module, make sure you have uninstalled that module. If you had search module enabled and if you are no longer using it, disabling it and uninstalling it will clear existing search index and now you could get a lot of database space saved.
If saving every bit of the space is worth, look at your third party libraries. They often come with folders such as docs and examples in it that actually do not help in terms of the site functionality.
Other places that you might want to check include, log folders (Apache logs), SSH command logs, old backups from Backup and Migrate module (or other backups), obsolete caches (Admin > Configuration > Development > Performance > Clear All Caches -- this will clear all caches, including in-use ones), watchdog (Administer > Reports > DB Log > Clear), spam comments (Admin > Content > Comments > Unapproved).
Make sure you keep a backup of the system for your own safety!