Hi Sten,
External codes are used to bridge the internal code to an external code. When looking at the screen above, you have an overview field and a value field. In the overview field you enter the general External Code group, like EAN / ISBN/ whatever. In the value field you enter the specific value for your tax code / related external code group. The setup here is not specific to tax and can be used throughout other fields using the external code functionality as Satish stated.
Although as far as I know (if someone does know please correct me) there are no default reports present for the Tax module using these external codes, you can off course make an entity export of this (relatedtable = 1472 // relation = recid of the sales tax code ). Besides this you can integrate this in the digital declarations to the VAT authority (setup under Tax --> Setup --> Electronic Messages). This uses the Electronic Reporting framework in which you can retrieve / translate the internal codes to the external code.
This should answer your second question, in regard to your first question, the bases for tax calculation is determined by the origin dropdown. The related document is always the bases, and for all of the options except for percentage of sales tax the line amount is taken as basis. If you would like to opt for sales tax on sales tax (like for example if you have packing duties which are taxable) then you can select the origin percentage of sales tax. After selecting this the box sales tax on sales tax becomes available in which you can select the base salex tax code it should start calculating on.
Keep in mind though, that even though the setup is sales tax on sales tax you still have to include both the original sales tax code as the sales tax on sales tax code in the same sales tax group / item tax group.
Hope this helps!
Best regards,
Ties Philippi