When bleeding radiator why does the same amount of water go out through the overflow?
It maybe that air got into the system and this is preventing the heating system to fill up properly. You may have to remove the air from the boiler itself, there should be a valve to enable you to do this. Replacing the pump seems to be either coincidental or unecessary. Also, when draing some or all of the radiators down it is advisable to put a chemical in to prevent any corrosive effect from taking place. This may have a minimal bearing on how hot the rads get, clean water in the system can encourage furring to take place and therby reduce the pipe thickness, again preventing enough water through to the rad.
Lastly, if the rad or system is old, you may have some thick sludge which will prevent the pipes and/or rad from getting any hot or cold water at all. depends on how thick the sludge is. The sludge could have been disturbed when the system was drained down.
To remove the sludge you can buy a chemical remover and put it into the rad which is worst effected and turn the heat on, then most suppliers recommend you drain the system and put a chemical in to prevent this again. Finally, I had to hit one rad because it was located in a room where i could not get to the valves. I kept on tapping it with a hammer to encourage the sludge to move on and into the outflow, with patience this did work but it did take 30 -40 minutes of tapping and bleeding.