Amphibious assault - what if no attacking land units survive

Hello, we are playing A&A 1942 2nd edition for the first time. So we are utter noobs. We did our best reading and analysing the rule book though, but still… :-)

During our game, Germany did an amphibious assault and attacked London. All attacking German land units that entered London from a transport ship got shot, but Germany won the assault (a lot of attacking planes destroyed all defending troops). So the situation is that London lost all of its defending troops (land and air units), but since Germany lost all its land units during combat and no attacking planes can land in London there are no German troops in London as well.

We have a few questions:

1. Is it correct to assume that Germany has conquered London since it won the battle, even though no attacking land units that offloaded into London survived the assault?
2. If so, Germany can take all of UK “unspent” IPCs?
3. Unspent IPCs = all IPCs that the UK has (so all the “money” that UK has, including all IPC that the UK got in the last step during the last time it was UKs turn)?
4. Can an enemy air unit alone conquer London in this situation? In other words: can air units conquer empty enemy territories without land troops supporting them? Can they attack them even if there are no units to attack? If so, is it just a matter of steps being able to take (e.g. 2 steps for a fighter to fly to London en 2 steps to land in a friendly zone)?

We would be really grafetul to get an answer. Thanks in advance!

Thank you all for your answers. That makes it clear: only land units can actually conquer enemy territories.

So then it is possible to attack land units in enemy territory with only air force just to destroy the enemy troops but without actually conquering the territory?