Is money lent by central banks to private banks counted in MB or M1? If a bank borrow money from a central bank but keeps it as a reserve instead of lending it to someone else, is it counted in the monetary base (MB) or money supply measure M1, using US definitions ?
Maybe that case just doesn't happen.

EDIT: A related question: if every debt is paid back (including money lent by central banks), does MB remain constant (which could not be the case according to the answer to the previous question) ?
Yes, it is in both but we have to be careful not to double count:


  The Fed’s definition of M1 is the sum of (1) currency outside bank
  vaults, (2) traveler's checks of nonbank issuers, (3) customers’demand
  deposits at commercial banks (with minor deductions), and (4) other
  checkable deposits, like negotiable order of withdrawal (NOW) and
  automatic transfer service (ATS) accounts. Basically, this is currency
  held by the public plus demand deposit balances outside the Fed. M2
  consists of M1 plus (1) savings deposits (including money market
  deposit accounts), (2) small-denomination time deposits (less than
  $100,000), and (3) balances in retail money market mutual funds.
  Individual retirement account (IRA) and Keogh account balances are
  excluded from M2. Excess reserves, required reserves, clearing
  balances held at the Federal Reserve banks, and the like, are
  components of the Fed’s monetary base but would constitute
  double-counting of the same factors if included in M1 and other
  monetary aggregates. Such accounts are readily spendable media of
  exchange (transaction accounts), but counterparts of these accounts
  already are included in M1, for example, as components of customers’
  demand deposits at commercial banks. The quantities of liquidity to
  fear for inflationary consequences are either monetary base or M1/M2,
  but not both simultaneously.


The Problem of Excess Reserves, Then and Now (Todd (2013))

What is the monetary base?


  In economics, the monetary base (also base money, money base,
  high-powered money, reserve money, outside money, central bank money
  or, in the UK, narrow money) in a country is defined as the portion of
  the commercial banks' reserves that are maintained in accounts with
  their central bank plus the total currency circulating in the public
  (which includes the currency, also known as vault cash, that is
  physically held in the banks' vault).
  
  The monetary base should not be confused with the money supply which
  consists of the total currency circulating in the public plus the
  non-bank deposits with commercial banks.


Wikipedia: Monetary base 

This is how it works:


  Creating Money through the Discount Window.  When a bank needs new
  reserves to support loans and investments it has already made or
  anticipates making, it ordinarily borrows from other banks at the
  Federal Funds rate.  But during times of stress, which are reflected
  by a shortage of liquidity in many banks, the whole banking system
  needs new reserves — hence the Fed's discount window. When a bank
  borrows funds overnight from the Fed's discount window (at an interest
  rate the Fed sets, called the discount rate), the bank's reserve
  account at the Fed is credited with the amount borrowed (and the Fed
  adds to its assets the additional amount owed to it by the borrowing
  bank).  Since the borrowing bank gets new reserves and no other bank
  lost reserves, net new reserves have been created for the banking
  system as a whole.  If the amount is also \$10 million, the banking
  system as a whole has a new capacity to expand loans and deposits by
  as much as \$100 million.  Thus, the Fed's open market purchases and
  discount window loans have the same ultimate impact on the money
  supply, at least until the discount window loans are repaid.


How the Fed Creates Money (McTeer and Villarreal (2008))