A lot of questions regarding lithium ion power supplies and power regulation with safeguards
Don't do this. It's a bad design!


You have more than one cell. Don't use the TP4056. It's a single cell-charger, and a less-than-perfect one at that. You don't want a lot of current going through linear regulators.  A good design wouldn't need a fan for cooling.
A proper battery management IC would make the relais unnecessary. And thus, save a lot of money in your design.
You want outputs that are all above your battery voltage. That requires stepping up. Stepping up takes place, cost, and efficiency. Avoid when possible. And it's easily possible here: just put your batteries in series to give you e.g. 6·3.7 V = 22.7 V and charge with a multi-cell charger IC.
5V 8A: That's an insufficient power supply. With linear regulators, charging your 8× 3.4 Ah will take eons. With more efficient switching regulators, still ages, if, and only if, your power supply doesn't give in: it's severly underdimenstioned for the job.
since you should be using cells in series, you'd normally just go for a cheaper, higher-voltage supply. What's wrong with 48 V? You can get such supplies cheaply; and then, feed switch-mode regulation from it.
Perfboard: nope. This is a high-current, explosion hazard if short-circuited design. It gets so much easier if you just layed out a PCB. Easier to design, since you can lay arbitrary thick traces. Easier to build, since you don't have to solder anything to connect things. Easier to test, becasue you can trust your traces to work. And safer. And saner. And prettier. Probably way more compact, too.


All in all, I think your design process was more like "I have this 5V supply, and I've heard of the TP4056, this must be the way to go" than "OK, I have these requirements, how do I fulfill them?".

That's a typical beginner's mistake – don't worry, we've all been there. So, take a step back. File your schematic under "learned a lot while drawing it, but not worth following"!

Start by making a proper list of what you want to do:


Which output voltages
Which output currents
Maximum instantaneous overall output power
Duration for how long you want to supply that


Based on that, decide on a multi-cell configuration that suits your needs.

Based on that, decide on output regulators that fulfill your needs (hint: drop the laptop charging idea. It's inefficient to discharge one battery to charge another, and laptops take a lot of current, so this is a very hard and expensive one to implement!) .

Based on the batteries, decide on a charger. There's multiple companies that build good charger ICs for multi-cell things. Maxim Integrated and Texas Instruments spring to mind; especially the MAX1640 might be the right choice for you. It can deal with 6 LiIon cells in series. At the powers you're dealing with, going with a linear regulator is really no option, so you'll need to go with the datasheet of the IC you select, and design a switch mode regulator. It's not that hard, but not trivial, either. Good news is that switching regulators are way more efficient than linear ones, so you might even get away without a single fan.

That also sets your charging voltage and current (hint: voltage will be a lot higher than 5V, and current potentially higher than 8A, too, depending on your design). Based on that, and thus, pretty much as last design step, choose a power source. It's not going to be your 5V 8A thing, whatever that was.

All in all, I think you might be underestimating the complexity of building the things you have planned. I think you even might have skipped the step where you roughly estimate how much power your primary power source can offer, and how much it'll take, even if you had 100% efficiency, to charge all your batteries (hint: energy = time · power= time · (voltage·current); energy in battery [Wh] = voltage [V] · capacity [Ah]; your 5V 8A supply only offers 5 V · 8A max = 40 W).