Passport got stamped and its dispatched back to VFS application center.
In case if the background check is not completed and they approve your eligibility for the application and made primary decision, they wait till the completion of background checks. These checks processing length varies from person to person so the time duration is variable.
About correspondence letter its very subjective. Normally they send correspondence after they made a preliminary or final decision on your application. Its either rejection or acceptance. If the case is straight like Yey or Ney , they send the decision very next day.Biometric enrollment form for VFS submissiom comes in 24 hours. The acknowledgement letter of Biometric has no timeline. Hope someome else in group may share their input.
In case if the background check is not completed and they approve your eligibility for the application and made primary decision, they wait till the completion of background checks. These checks processing length varies from person to person so the time duration is variable.