The most common way to put down tracks – normally we put down drums first then bass (quite often together as well), guitars and keys and finally vocals and backing vocals. We often have various combinations of band members playing along so we still achieve a good performance style. Complete separation isn't always the best way to get a great feel to the recording - but it does work for some - we'll happily work with a band to get the best results.
Time taken to get a track recorded and mixed can vary depending on how complex the arrangements and number of instruments to record, overdubs, fx etc but with minimal takes you could expect to get a rough mix of two tracks done in a normal day.
Additional time would generally be needed for final post-production/mixing and mastering.