Mid 2012 Macbook air battery charging erratically

Question

A few days ago, I noticed that my macbook air was not charging even though it was plugged to the power adapter. After some time, it showed that it was charging, but infinitely slowly. I did SMC reset and after a while, it was charging normally. But the problem reappeared some time later. Some times SMC reset seems to help, some times it does not. Some times it says that the battery is charged, while the battery percentage is showing less than 100. Also, the connecter light is also not synchronous with the battery state sometimes.
I had changed the battery a couple of months ago. The power adapter is also new. Also, I some times hear a very low buzz sound coming from the connector of the adapter.
Battery Information:
  Model Information:
  Serial Number: D86129705HXDKRNAL
  Manufacturer: SMP
  Device Name: bq20z451
  Pack Lot Code: 0
  PCB Lot Code: 0
  Firmware Version: 406
  Hardware Revision: 1
  Cell Revision: 162
  Charge Information:
  Charge Remaining (mAh): 5769
  Fully Charged: No
  Charging: Yes
  Full Charge Capacity (mAh): 6274
  Health Information:
  Cycle Count: 53
  Condition: Normal
  Battery Installed: Yes
  Amperage (mA): -166
  Voltage (mV): 8152
System Power Settings:
  AC Power:
  System Sleep Timer (Minutes): 10
  Disk Sleep Timer (Minutes): 10
  Display Sleep Timer (Minutes): 10
  Wake on AC Change: No
  Wake on Clamshell Open: Yes
  Wake on LAN: Yes
  AutoPowerOff Delay: 14400
  AutoPowerOff Enabled: 1
  Current Power Source: Yes
  DarkWakeBackgroundTasks: 1
  Display Sleep Uses Dim: Yes
  PrioritizeNetworkReachabilityOverSleep: 0
  Standby Delay: 4200
  Standby Enabled: 1
  Battery Power:
  System Sleep Timer (Minutes): 10
  Disk Sleep Timer (Minutes): 10
  Display Sleep Timer (Minutes): 2
  Wake on AC Change: No
  Wake on Clamshell Open: Yes
  AutoPowerOff Delay: 14400
  AutoPowerOff Enabled: 1
  DarkWakeBackgroundTasks: 0
  Display Sleep Uses Dim: Yes
  Reduce Brightness: Yes
  Standby Delay: 4200
  Standby Enabled: 1
Hardware Configuration:
  UPS Installed: No
AC Charger Information:
  Connected: Yes
  ID: 0x0000
  Revision: 0x0000
  Family: 0x0000
  Serial Number: 0x00000000
  Charging: Yes

Answer 1

Assuming you have the tools required (two different screw drivers and a plastic tool to lift the connector from the logic board) you will save about $30. If you don't have, or don't have access to the tools you'll save almost nothing. However, depending on your source you may wind up with a counterfeit Apple battery, a used battery, or a battery that may or may not be truly Apple compatible. Take it to an Apple Store.