Updated : 25/04/2017
YES / NO — You cannot be made to pay VAT in more than one country, and VAT on cars is payable in the country where they are to be registered, i.e. France (not in the country where they are bought — the rule for most other goods).
You could have told the dealer that the car was intended for registration in France, and avoided paying Belgian VAT.
Since you already have paid Belgian VAT, you should now apply for a VAT refund from the Belgian tax authorities, based on evidence from the French authorities that you have registered your car in France within 6 months of it first being put on the road and before it has clocked up 6,000 kilometres.
Although the car will eventually have to be registered in France, you still need to get German licence plates to drive it back to France. If the car is new, you should get transit licence plates — this will also allow you to avoid having to pay VAT in Germany. If it is a used car, you will probably have to get ordinary German registration, even for a short period. Consider having the car shipped to you in France, so you don't need to register it in Germany, and compare the costs.
Import duties have been abolished within the EU. Perhaps the charges are in fact vehicle registration and road taxes — payable on all cars registered in a given country, regardless of where they come from. These taxes are not regulated by EU law, and you must pay them — provided they do not discriminate against imported cars. For instance, the registration tax should not be higher than the tax value of a similar car already registered in Malta.
Passenger car registration tax is not harmonized at EU level. EU countries are therefore free to levy a registration tax when a car is registered on their territory for the first time. Because of the disadvantages for people in your situation, it is currently up to each EU country to decide whether to grant an exemption for cars moved in connection with the owner's change of residence. You should contact the Portuguese authorities to find out whether your case qualifies for such an exemption, and if so, under what conditions.
NO—Just tell the German seller you are going to register the car in another country. You will then only pay VAT in Holland.