While the R and RStudio programs themselves are installed on the C:/ drive, your R packages (rstan, etc.) are installed in your ‘Home’ directory, which the error message above indicates is on an external network drive (\home.org.aalto.fi/alonzoi1/data/Documents). You need to move your R packages to a folder on your local C:/ Drive.
I posted some instructions on how to do this over in this post. Those instructions were putting the R packages in the C:/Users/R folder, so just change that path to wherever you want to move your R packages to