Magento 2 – Which Database Table Stores the Attribute Position?

I think i can help you here.

What i can see here is you need something like brands listing which are configured as an attribute i.e manufacturer in back-end so that when admin sets the manufacturer for the product that product appears when some one click on that manufacturer's label and before that all the manufacturers are listed.

If there is anything more tell me i will provide you the code snippet here. Also tell me how far you have reached.

If you got orphan attribute values it means that there is something wrong with your database.
For example the table catalog_category_int has a constraint on the attribute_id column.

CONSTRAINT `FK_CAT_CTGR_ENTT_INT_ATTR_ID_EAV_ATTR_ATTR_ID` FOREIGN KEY (`attribute_id`) REFERENCES `eav_attribute` (`attribute_id`) ON DELETE CASCADE ON UPDATE CASCADE,

This means that if the attribute is deleted, all the values for the attribute from the table catalog_category_int will be deleted.
It's the same for the rest of the tables (catalog_category_*).

From experience I saw that usually constraints are lost during a migration process. You export the database but without the constraints. If this is the case then remember in the future to use System->Tools->Backupto create database dumps for migration.

[EDIT]
Here is the code I've used. I've created a simple extension that adds an attribute to the category entity, I edited a category and filled in a value for that attribute, then deleted the attribute through an upgrade script.
Here are the extension files:

app/etc/module/Easylife_Attr.xml - declaration file

<?xml version="1.0"?>
<config>
    <modules>
        <Easylife_Attr>
            <codePool>local</codePool>
            <active>true</active>
            <depends>
                <Mage_Catalog />
            </depends>
        </Easylife_Attr>
    </modules>
</config>

app/code/local/Easylife/Attr/etc/config.xml - the configuration file

<?xml version="1.0"?>
<config>
    <modules>
        <Easylife_Attr>
            <version>0.0.1</version>
        </Easylife_Attr>
    </modules>
    <global>
        <resources>
            <easylife_attr_setup>
                <setup>
                    <module>Easylife_Attr</module>
                    <class>Mage_Catalog_Model_Resource_Setup</class>
                </setup>
            </easylife_attr_setup>
        </resources>
    </global>
</config>

app/code/local/Easylife/Attr/sql/easylife_attr_setup/install-0.0.1.php - the install script

<?php

$this->addAttribute('catalog_category', 'dummy', array(
    'group'         => 'General',
    'input'         => 'textarea',
    'type'          => 'text', //can be any type
    'label'         => 'Custom attribute',
    'backend'       => '',
    'visible'       => true,
    'required'      => false,
    'visible_on_front' => true,
    'global'        => Mage_Catalog_Model_Resource_Eav_Attribute::SCOPE_GLOBAL
));

Now add a value for this dummy attribute for a category.
You should see it in the table catalog_category_entity_text.

After that create an upgrade script to remove the attribute. app/code/local/Easylife/Attr/sql/easylife_attr_setup/upgrade-0.0.1-0.0.2.php

<?php
$this->removeAttribute('catalog_category', 'dummy');

and change in config.xml the version from 0.0.1 to 0.0.2.

Refresh any page and look in the same table catalog_category_entity_text. The value that was added for the dummy attribute is gone. (at least for me).