What changes were made to the 777 as a result of British Airways 38?
The aircraft accident was caused by ice accumulating in the Fuel Oil Heat Exchanger (FOHE) of the Rolls-Royce Trent 800 engines which subsequently blocked fuel flow to the engines. The official accident investigation concluded:


  The investigation identified the following probable causal factors that led to the fuel flow restrictions:
  
  
  Accreted ice from within the fuel system released, causing a restriction to the engine fuel flow at the face of the FOHE, on both of the engines.
  Ice had formed within the fuel system, from water that occurred naturally in the fuel, whilst the aircraft operated with low fuel flows over a long period and the localised fuel temperatures were in an area described as the ‘sticky range’.
  The FOHE, although compliant with the applicable certification requirements, was shown to be susceptible to restriction when presented with soft ice in a high concentration, with a fuel temperature that is below -10°C and a fuel flow above flight idle.
  Certification requirements, with which the aircraft and engine fuel systems had to comply, did not take account of this phenomenon as the risk was unrecognised at that time.
  


(official accident report summary)


(image source: official accident report)

The FAA issued an amendment to an older Airworthiness Directive (AD) in March 2009:


  Boeing Model 777-200 and -300 Series Airplanes Equipped With
  Rolls-Royce Model RB211-TRENT 800 Series Engines
  
  [...]
  
  SUMMARY: The FAA is superseding an existing airworthiness directive (AD) that applies to
  certain Boeing Model 777-200 and -300 series airplanes. The existing AD currently requires revising
  the airplane flight manual (AFM) to include in-flight procedures for pilots to follow in certain cold
  weather conditions and requires fuel circulation procedures on the ground when certain conditions
  exist. This new AD retains the fuel circulation procedures. This new AD also revises the AFM
  procedures required by the existing AD. This AD results from a report of a single-engine rollback as
  a result of ice blocking the fuel oil heat exchanger. We are issuing this AD to prevent ice from
  accumulating in the main tank fuel feed system, which, when released, could result in a restriction in
  the engine fuel system. Such a restriction could result in failure to achieve a commanded thrust, and
  consequent forced landing of the airplane.


(AD 2009-05-11)

The NTSB then requested a redesign of the FOHE from Rolls-Royce:


  The US National Transportation Safety Board (NTSB) on 11 March released urgent safety recommendations for the redesign by Rolls-Royce of the fuel-oil heat exchanger on Trent 800 engines powering Boeing 777s.
  
  NTSB says Rolls-Royce is already working on a redesign that could be available in twelve months, but still felt compelled outline the need for the heat exchanger overhaul.


(flightglobal.com)

In Europe, EASA required the new FOHE to be installed since January 2011 at the latest:


  Reason:
  
  This Airworthiness Directive has been raised following an incident involving dual
  loss of engine response in the final stages of approach leading to touchdown
  short of the runway. The phenomenon involved in the loss of engine response
  has also been seen in flight affecting just one engine.
  
  Post incident analysis and investigation has established that, under certain
  ambient conditions, ice can accumulate on the walls of the fuel pipes within the
  aircraft fuel system, which can then be released downstream when fuel flow
  demand is increased. This released ice can then collect on the FOHE front face
  and limit fuel flow through the FOHE. This type of icing event was previously
  unknown and creates ice concentrations in the fuel system beyond those
  specified in the certification requirements.
  
  To mitigate the risk of dual engine FOHE blockage within the Trent 800 engine
  powered Boeing 777 fleet, which constitutes a potential unsafe condition, this
  Airworthiness Directive instructs replacement of the FOHE with a modified
  standard incorporating enhanced anti-icing and de-icing performance.
  
  Required Action(s) and Compliance Time(s):
  
  Within 6 000 flight hours from 10 July 2009 or before 01 January 2011,
  whichever occurs first:
  
  Replace the FOHE with an FOHE modified in accordance with RollsRoyce Alert Service Bulletin RB211-79-AG257, dated 24 June 2009
  (published 10 July 2009).


(EASA AD 2009-0142)

Regarding your bonus question: Yes, there was another incident (Delta Air Lines Flight 18, 26 November 2008) where ice accumulation in the FOHE resulted in an engine rollback (luckily only one engine this time):


  Since we issued AD 2008-19-04, we received a report of a single-engine rollback as a result of
  ice blocking the fuel oil heat exchanger (FOHE) on a Model 777 airplane equipped with Rolls-Royce
  Model RB211-TRENT 800 series engines. The data confirm that ice accumulates in the fuel feed
  system and releases after a high thrust command, creating blockage at the FOHE and resulting in the
  inability of the engine to achieve the commanded thrust. Examination of the data from the rollback
  shows that the second of two maximum thrust step climbs was performed approximately 40 minutes
  prior to the thrust rollback. Ice was released within the fuel system during the step climbs and formed
  a restriction at the FOHE of the affected engine, as evidenced by an increase in engine oil
  temperature.


(AD 2009-05-11)