Only the diagram is slightly wrong. See the correct one attached.
Back to the questions
1) 6W @ 5V => 1,2A, 6W @ 2,3V (li-ion minimum of the module) 2,6A. So a 3A diode should hold. But it can get quite hot because it will dissipate 1,3W...
2) Because diagram was wrong ;)
3) They will, but the voltage drop over them is a lot bigger. And when dealing with batteries that's a bad thing most of the time. The reverse leakage current is a bit higher but that's not a problem.
Ow, and be aware your power supply needs to be able to deliver the 6W for the circuit AND the 1A of the charge at the same time.
[Edit] Now with a image...
Thanks for the info,
I have a few more doubts.
1)Heat is not a problem for my project, but will mentioned diode ever get so hot that it starts smoking and gets damaged if I use 24x7(since its UPS)? Do you have any other diode model in mind?
2)Are you sure reverse leakage from Schottky wont cause any harm to batteries or other components?
3)My power supply is a 5V 2A USB Wall adapter (10W). Can I make it fully power my device giving it more priority and give only whatever remaining power available to battery charger?
4)If above mentioned method is not possible then can I limit the current going into the TP4056 battery charger to 200mA or so?., No problem if battery takes longer time to recharge but max power going for the Load is a priority when main power is available.
4)Is there a max current limit for the OUT terminals of the TP4056 module? If it has like 1A or below then should I bypass the OUT terminal and connect directly to battery to get more current?