1) Caution is already there in the manual that accompanies it. 2) Yes, it is uF value. 3) Yes, resistor is for discharging residual charge. 3) Nothing! USB is not isolated! That is the funny thing in this! 4) No primary fuse either! Many thanks!

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No problem Parasuraman, I understand the electronic circuit now. Thank you for the clear explanation. I hope that no one is able to touch any of the wires inside or the circuit while charging it on 230VAC. Or takes out or puts in any of the rechargeable batteries which could be fatal of course!
The resistor over the Capacitor of 1.5uF (and not miliFarad.. which would make the Xc resistance with a value of only 1/(2xPixfxC) = 2.12 Ohm much too low instead of 2.122 Kohm) is of course for discharging any high voltage charge that it still contains after disconnecting the lamp from the AC main power. I think it probably also has some kind of switch to disable the 230V AC when the USB charger connection is used (or is there only a warning on the outside of the lamp written?). And it should have a primary Fuse too to prevent causing any fire.
To prevent any oxidation on components and wires I used clear varnish to protect the inside electronic circuit of my Solar lamps. Also on the ordinary two legged white leds in my solar lamps because the legs were mostly badly damaged and couldn't be soldered afterwards. Cheers!

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Really enjoy the thoroughness that you approach your projects with,  it's like a scientist looking into the unknown, or a doctor looking for a cure!  A sure path to success.  It is satisfying to resurrect a device headed for the void. Job well done.

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Many thanks for your detailed observations and suggestions. The LEDs and board were all bad spoiled by the battery acid. IPA stands for isopropyl alcohol. I indeed took a close shot of the board from the components, but while transferring it from mobile to computer, it was missed and I have no clue why. Since these are old, I could not locate it again in my mobile and probably it could have got erased when I purge all unwanted images from the storage. The circuit is very simple, like any chinese lamp. 230V AC is directly fed to the board, one side through a capacitor dropping the voltage to the required limit. Both these AC inputs (one direct and another through this capacitor, are fed to bridge rectifier, and smoothed by a 47mfd/25V capacitor. A 1k resistor is used to control current and voltage to the LED. The battery is directly connected to the +/-, the LEDs via the on off switch at the bottom. The solar input is fed, - directly and the + through IN4007 diode. This is to enable charging depending on the potential. USB charger is wired from the battery directly. There is nothing complicated in this circuit. There is no over voltage protection, battery charge limiter or any such thing! There is a charge dropping resistor of high value (I think it was some 470K) connected across the Fixed Capacitor used for dropping AC input. I think it was a 1.5mfd Fixed Capacitor. That is all! As for the water seepage inside, I had cautioned the customer about what had spoiled the lamp and asked them not to keep near windows (which was the cause for rain water seeping in) for two reasons (1) over charging from direct sun light and (2) Water seepage. I did not cover the sides as there are small holes there for ventilation and battery fumes to go out.

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