Firstly, please add more information:
What is to make and model of you bike?
What are the exact modifications you've done (with spec of the components)?
Now, when you say "under full load" I assume that you mean with all optional electrical system on and at full settings (like with the high beam on). If that's what you mean, then your horn will function quietly/low because another part of the system is drawing too much amperage and your horn, therefore, can't get the energy it needs to fully function.
Now consider, if your old headlight was AC, and you used a rectifier to make the new on DC, then rectifier is adding new resistance, and thus amp draw, of that line. Now also you've upped your headlight from 35w/35w (2.9A/2.9A) to 60w/55w (5A/4.6A). So just based on the new lamp, you're drawing 9.6A on the headlight alone! That's a lot more that the 5.8A that was factory.
So, for your questions:
If I have upgraded the coil winding, to supply more current/power, then whether, my Rectifier can withstand?
This depends on the specs of your rectifier.
Battery will damage/become weak if I have supplied more power to it?
Modifying your recharge system could severely damage your battery if not done correctly, and could risk causing a battery explosion. Minimally, it's likely to reduce the life of the battery somewhat. The reason the stock system will be lower amperage than the battery is to have more of a "trickle" effect. This is a better way to recharge in terms of health. Allowing too rapid a charge (I.e. Higher amperage) will cause the battery to get hotter. In many cases this won't be an issue, but when your battery starts to get old this will become increasingly risky as it won't hold full charge and will draw more from your recharge system.
And also I have heared that, coil rewinding will change some ignition timing, Is it so?
It should not affect timing. The timing is based off of the mechanical action of the motor, so changing electrical items should not affect it at all.
Do I need to change the Fuse, since only 10A fuse is mentioned in my bike. Will it get fused if more current comes? Is there any way to deal with this?
This why is we need the make/model info. I have no idea where this fuse is that you're talking about, but there has to be more than one. To facilitate your current configuration, you will have to up the fuse - however - doing this can create a serious risk to all other components on the same fused circuit or section!!! The fuse is there to protect items from getting too much juice, so increasing the fuse rating to allow for a brighter headlight will also mean that other items (possibly your horn, blinkers, tail/brake light etc.) at greater risk of overload as well.
But the existing alternator is generating only 100/12 = 8.33 Amps, in which my existing battery is stated to give 9Amps. Is there any safety/particular reason, Why the factory packed alternator is supposed to give the less Amps.
As I mentioned above, it's partly because of health and safety for your battery and other parts, but also for simplicity. If your whole electrical system will function on < 10A, why would they give more? Also, what do your mean by 100/12 = 8.33 Amp?
After looking at your specs a bit, I'd say to get something like this LED H4 headlight. The overall power use is 42W combined, so you'd drop below your stock usages. Which would mean that you bike is now producing more than is needed. This would be a savings of ~73W overall (though my math method could be wrong).
- LED - 24W + 18W = 42W overall
- Halogen - 60W + 55W = 115W overall
Rewinding the coils is a lot of work, is not easy to do, and the problem is solved more easily by reducing your overall consumption. That said, one of the main points of concern that I've seen in other thread regarding increasing lamp brightness, is the melting of conductors (wires) and light socket/boot. This is because a higher brightness light (especially true with Halogen and HID lights) will produce much more heat. Under worse-case-scenario conditions this could result in a fire because of burning the insulators or other plastic parts. So, not only would you have to re-wind your coils, but you'd also have to redo a good bit of wiring to be safe.
NOTE: I have no practical experience with LED headlights, nor am I recommending the above lamp over any others! It is also very important that you check what your local laws are regarding headlight colors and brightness. This may not be a concern wherever you are, but is some locals there are strict regulations on it and you can (and possibly will) get ticketed for it.
Also, I Googled "halogen HS 12v 35/35 light" and the results indicated a 12VDC lamp... are you sure that you were actually getting AC at the light before? Or did you assume that because "generator" output AC that it was getting AC at the lamp? From my understanding the vast majority of the electrical system has a stock rectifier between it and the stator... even alternators to my understanding often have a rectifier built into them so that the unit outputs DC voltage.