Can I ask the German company to help me with expenses of housing to be able to move if they need me in another country in Europe?
Companies handle business trip expenses in one of the following ways :
- The company provides the housing / ticket / food
You have nothing to do. This is legally considered tax free.
- The company refund the expense
In this case, you should keep all justificative documents and get refunded back by your company for your expenses.
- The company gives you a package for this expense
If you take your own car, your expenses are legally covered by 0.30€ per kilometer. Food can be also covered by a package based on the length of your stay. This is free of taxes, again.
And if in doubt of how the company will handle a fee, the best thing might be just to ask them.
In case you are moving permanently, this is different. You need to renegociate your contract with the new location, including if appliable a different pay and other benefits the company might provide for relocation (company policy here, nothing legally granted).
In all cases, if the conditions aren't favorable, you can always decline a permanent relocation offer as any other renegociation of your contract.