Fixing a wall-wart?
I have a wall-wart that is working but I'm having some problems with it. It coverts 220AC to 10VDC with 1,3A current. I've been using it mainly to power up 8cm PC fans. Recently I opened it up and saw that below the diodes,board has turned black and it seems fried, that can be from excessive heat generated by diodes, and part of the transformer that was facing this diodes is melted (as you can see in pictures). I think diodes are 1n4005.
1- my first questions is, why these diodes got this hot ? should I change them with diodes that can pass more current? I have RL205 will that work?
2- I've read somewhere that after rectifier bridge, if capacitor's capacity is high, it will put pressure on diodes and transformer, is this true ? or we can use any high capacitor we can find ?
3- Is there a law by which we figure out how high our capacitor should be after rectifier bridge in wall-warts ? for example If I had a wall-wart with 1000mF capacitor, can I change it to 2200mF ?
4- I am going to use this wall-wart to power up a 7805 regulator, so that I can feed a lithium-ion battery charger module (4056). This module uses 1A. should I put a high value capacitor like 470mF or more, at regulator's input, or is it unnecessary cause of my wall-wart having a high capacitor ?
5- Are they any ways that I can improve this wall-wart ? like if I keep the transformer cool ,when it;s under load ...maybe add another capacitor ... ?