I bought few LiIon modules(TP4056, from eBay). Every module has 1.2kOhm resistor, so module will charge batteries(six in parallel) with maximum 1A. Because I have 42Wh power source, it'll take around 30 hours to charge from ~0% to 100%. So my idea is to use three TP4056 connected in parallel with batteries. Does it will work without blowing up batteries? Schematic is below(MT3608 is step-up booster). Batteries are from my old laptop's battery, they are without Protection. Also, I won't use TP4056's Protection. At best scenario, batteries will get 0.4A of current(2400mA divided by six batteries).
No. As its data sheet tells you in the first line, the TP4056 is designed to do one thing and one thing only: charge a single cell Li-ion battery. The 1k2 resistor allows you to change the charging current so you can safely charge a larger battery in the same time as a smaller one, but that's all you can do with it.
You can't combine its output with another output, which is something you can rarely do with any circuit that's not been specifically designed to allow you to do this. And you can't charge a battery at the same time as drawing power from it as you're showing in your diagram, because that's a physical impossibility. The charging circuit should be disconnected when you want to draw power from the battery (the TP4056 contains a blocking diode so that you can leave it connected to the battery and just remove the USB plug), and the reason for this is that the charger controls and monitors both the charge current and voltage in order to charge the battery correctly and safely, and connecting anything apart from one battery gives the charger no way of knowing what load is down to the battery and what is down to the other device.
So if you want to charge six cells at once, use six TP4056s, they cost peanuts compared to the batteries themselves. And make sure your power supply and connectors can safely handle the maximum current, because a mini USB is going to struggle to cope with 6 Amps.