Charles Lyells book 'Principles of Geology' explains that all sedimentary rocks are deposited by extremely slow processes, such as rain washing loose sand down a mountain slope to a river.
No, it doesn't. It explains that all geological phenomena are explicable by processes that continue today. Much of that is extremely slow, but Lyell
most certainly does not exclude the operation of rapid forces - in fact much of the Principles is occupied with discussion events such as volcanoes and earthquakes. Floods and landslides are also discussed.
Is this theory still current today? Or has it changed?
Much of what Lyell outlined has survived, but it has tested, refined and greatly expanded upon. Among the most important principles included since Lyell's time are Evolution, Plate Tectonics and Radiometric dating.
the other thing i want to know is why geology and evolution are so closely linked? Shouldn't they be independent of each other?
Had the Earth been created then perhaps that would be so, but since it was not, the two are strongly linked. Biological forms are a very important driver of important geological factors - I'd highlight chalk beds*, and banded iron formations** as the most clear cut examples - and because of the continual change of organisms driven by evolution they provide clear dating means.
* - formed from the microscopic shells of trillions upon trillions of coccoliths.
** - formed by the oxidation of Iron caused by the release of oxygen into the atmosphere by microbial photosynthesis.
Edited by Mr Jack, : Typo