Rust in BB / steel frame

Hello Everyone, I noticed some grinding sounds and clickling coming from my bottom bracket, therefore I decided to replace it. It was a BB-52 from Shimano and it lasted around 3800 km. I think thats a bit early but nothing to worry about?

Now, after removing the BB, I noticed quite a bit of rust that likely came from the old shells (first two pictures). After some brushing and cleaning, I got most of it removed (next two pictures). I think it should be fine to put grease all over the bottom bracket housing and install the new BB?

The last picture shows the view down the seat tube, which also contains some rust, but I think thats also nothing to worry about, right?

Thanks for your Help!