Yes, the Item Tax Setup is rather counter-intuitive, the only reason the item taxes are defined this way so far is backward compatibility.
Anyway, if you want to have GST calculated on Item sold to Customer, the same non-zero GST rate have to be set for both:
a. Item Tax Group the item belongs to;
b. Tax Group assigned to your customer branch.
It means that in case a) you have to untick the related tax type, in case b) you have leave the box ticked.
Now about sales prices, in Sales Types you can define two kinds of pricelists: with tax included, or tax added.
Example:
. GST rate 5%.
. base invoice price $100.
When the price list has 'Tax included' box ticked final item price is $100 = 95.24+5%GST, otherwise tax is added to the price, so final price is: $105 = 100+5%GST.
All the other FA settings are not relevant to the tax calculations, so if you configure your system as described - it just have to work.
Janusz