Hi Mathias and welcome to the forum,
I'll try to cover all your questions, but there are a few, so forgive me if I miss one :)
1. Do you need a licence to dropship internationall?
No licence required, what you will need with some suppliers is a local tax id to prove you are a legit trader.
2. Do you need to register a business?
This really comes down to the supplier you are going to deal with. If they require a tax id, like many do, then yes, you will need to have a legit tax id. Now I'm not sure what the laws are in Norway, perhaps you can secure a tax id without actually registering a business. So I would suggest just calling your local authority and double checking that one.
3. Regarding Sole Propiertor?
If you are going to be trading as a single entity, then I would suggest you should register as a SP if you do register, but again, best to double check with your local authority in case there is a more applicable option for you to choose.
4. Different licences to sell internationally?
No, no licence is required to sell at all online, locally or internationally. Only two things you need to be aware of, your local business registration tax laws.
Your Value Added Tax is only for imports. Anything you sell into another country is subject to that counties own tax laws.
6. Trading through eBay
No licence required, all you do is register for free with eBay.