Deleting Content Manually If I were to delete the latest row of the node table in the database would all traces of the latest added content be gone from my site without errors from core modules after clearing the cache?
If you delete a row directly from the node table you can expect:


At best - you will just have a bunch of orphaned data in the system. Tables containing this orphaned data include, but are by no means limited to,


node_revision
taxonomy_index
url_alias
search_node_links
Any number of field_data_FIELD_NAME and field_revision_FIELD_NAME tables


Those are just a few of the core tables that can be affected; there are others, and many contrib modules will install tables to store node-related data. Those will also potentially contain orphaned data.
At worst - there's no telling how this could affect your site, it completely depends on how it's configured. You might get lucky and experience nothing but the orphaned data, but I wouldn't advise counting on that. Before you do anything, take a backup of your data.