Very good question(s) since I asked them myself but never made the effort to research the answer(s). To answer yours:
Does this Purity Law extend to process thereby making every German Beer vegan?
There is an official website stating:
Deutsche Biere sind vegetarisch und vegan. Bei der Bierherstellung werden keine tierischen Stoffe eingesetzt. Das auf dem Reinheitsgebot basierende Vorläufige Biergesetz und die Bierverordnung geben klare Vorgaben für die Herstellung von Bier, wonach tierische Stoffe wie Gelatine oder Hausenblase nicht zulässig sind. Was man aber wissen sollte ist, dass einige Etikettenleime Casein tierischen Ursprungs (Proteine aus der Milch) enthalten können.
Which means (almost perfectly translated via DeepL):
German beers are vegetarian and vegan. No animal substances are used in the production of beer. The Preliminary Beer Act, which is based on the Purity Law, and the Beer Ordinance provide clear guidelines for the production of beer, according to which animal substances such as gelatine or isinglass are not permitted. What one should know however is that some label glues can contain casein of animal origin (proteins from the milk).
What exceptions should I look out for when drinking beer in Germany?
This is also answered on the website:
Is it permitted to brew beers in Germany that do not comply with the Purity Law?
Yes, there is an exception for so-called "special beers" in the Act (§ 9 Paragraph 7 Provisional Beer Act). This regulation applies to all federal states except Bavaria. This enables brewers to produce beers with spices such as anise, cinnamon or cloves as well as fruits such as orange or cherry. Well-known beer styles that have always deviated from the strict purity law include Berliner Weiße and Leipziger Gose. According to the existing law, only those additional ingredients may be used that give the beer a special character or taste. Malt or hop substitutes are also not permitted for "special beers". In addition, it is permitted to deviate from the purity requirement for beers for export. "Special beers" and beers for export that deviate from the Purity Law must be approved by the relevant state authorities. Those who do not brew more than 200 litres of beer per year at home do not have to comply with the Purity Law either.
Do the same laws apply to German beers produced for export?
This is answered above: "In addition, it is permitted to deviate from the purity requirement for beers for export. "Special beers" and beers for export that deviate from the Purity Law must be approved by the relevant state authorities."