In theory. In practice roads between counties are not as good so cost goes up.
One of the EU projects is trying to improve the transport links (including road network) between EU countries – https://ec.europa.eu/transport/themes/infrastructure/ten-t_e...
One would hope that if they are successful in improving those transport links, shipping costs will reduce as a result.
Somewhat. Population also tends to be centered around the country so it even if transportation is better people still have their lives setup such that practically shipping in their country is cheaper.
In principle, shouldn't one of the consequences of the EU project be that intra-EU shipping rates should, for the same distance, be identical between within the same country and between EU countries? (Of course, I realise that outcome may not yet have actually been achieved in practice.)