Will this 18650 tp4056 parallel circuit work for charging and simultaneous power supply or will things break?
Your new and improved schematic shows that you have parallel connected the batteries and charger outputs. There is no way for each charger to know which battery is being charged.



Figure 1. The only circuit given in the TP4056 datasheet.

With only one example application that datasheet doesn't give a lot of help. I'd look around for a similar chip with more sample applications.