Can the German company make a claim through the British Small Claims Court or do have to use the EU Small Claims Court system?
I believe you can, but you are likely to have to travel to the UK if a hearing is needed. The EU system is designed to work from documents where possible and hence not need a hearing.
You can. The claimant need not be present or domiciled within the UK for proceedings to be issued and served (since by issuing proceedings the Claimant thereby submits to the jurisdiction of the English courts)
As long as the defendant in this action is domiciled in the UK (for a company, this would be that they are registered in the UK, or that their principal place of business is in the UK, or that they have a registered branch office in the UK) you may serve proceedings on them. (You can also sue a foreign company in england, but that requires court permission)
See CPR 6, which governs service, for more information