Influence on contemporary cinema

Ridley Scott’s blade runner (1982) was heavily influenced by the German expressionist film movement taking imitated sequences from other German Expressionist films. Bladerunner’s emphasis on the degraded, alienating city resembled that of many expressionist “street films” taken together. Some propose that “Bladerunner” was a remake of Lang’s Metropolis.

Blade Runner (1982) - IMDb
Los Angeles, 'Blade Runner,' and the Theory of Relativity | WIRED
Fritz Lang's Metropolis: A Reflection of a Restless Time — Stéphanie Ruth

Influence on hollywood – film noir

As with both styles of films, film noir is influenced by German Expressionism with its dark shadows and sharp lines. As in many films, Film Noir focuses on low key lighting, monochrome colours, and abstract angles. Films were made using a variety of techniques to convey their genre and themes.

The Night of the Hunter (1955) | The Criterion Collection
Saul Bass | Saul bass, Vertigo movie, Vertigo poster
The Maltese Falcon (1941) - IMDb
The maltese falcon- 1941 ( John Huston)

how is the ufa still in business?

The purpose of the UFA was to promote Germany during WW1. Due to a financial collapse in the film industry the UFA was about to head into financial ruin when a powerful financier Alfred Hugenberg, a future Hitler supported, brought the place in 1927. He made to company indulge itself into films the promoted German nationalism.

When the Nazis came into power in 1933 films became promotions to the general public about the Nazis also known as Nazification. Without promoting Nazi Germany then the UFA wouldn’t have stayed in business and used tactical ways to continue to produce films during the war era.

UFA-Wocheschau (Germany) - CLG Wiki
Movies of a turbulent century: German film company Ufa turns 100 | Film |  DW | 18.12.2017