I'm a client and a digital agency (in the UK, I'm in Germany) will do some graphic designs for me. Which kind of contract is usually used for this? Who makes it? Which laws do apply for payment, accountability, VAT etc? I don't need a lawyer answer, just some orientation, or links, because I have no idea at all.
You will be charged VAT if the company that is developing your deliverables is VAT registered... (Not all companies are, and they do not have to be under certain conditions). If you are charged VAT, ensure that you receive a VAT receipt, this will allow you to claim back the VAT if your company is also VAT registered. If you're not VAT registered, you will not be eligible to claim back VAT.
Laws regarding payment is wholly dependent on the contract that you agree on with the company that is developing your work. If you agree to 50% now, 50% upon completion and have it in writing then that is what will be expected. You also need to define and agree on what "completed" means and have a contract drawn up from that, eSignatures are valid and legally binding and if you hate reading terms and conditions, this is probably the one time you won't want to skip on reading it.