The box size would be height=400mm, length=800mm, width=400mm, made of 10mm plywood. Say the max load on boxes when used as benches = turned open side down is 200kg and the load when used as a box is 50kg max.
I'm going to convert to Imperial units since that's how my brain works. This is about 16" x 32" x 16" and 3/8" plywood, supporting 440 lbs when overturned and 100 lbs when used to carry items.
The 400mm span might be a bit much to carry 200kg using only 10mm plywood. Are you really expecting that a 200-kg person will sit on this? Anyone I know that's that obese would have a hard time sitting on a box this low. Otherwise, 800mm isn't really wide enough for two people to sit next to each other (unless they're quite friendly or very skinny).
Likewise, I doubt anyone is going to be able to (easily) carry 50kgs of stuff in that box. I know in the US, lifting weights for most jobs are limited by OSHA to 50 lbs (22 kg). Even that is quite a bit of weight for what I assume are casual storage boxes.
That out of the way, let's delve into your three bullet points.
I can think of 3 methods of making a corner joint, I want to choose based on labor time and cost given they are made to provide same strength.
- Inside corner brackets. -- how many brackets do I need, what's optimal screw size?
I would say (3) brackets per corner, one at the top, middle, and bottom of the joint, should be sufficient given your loading and proposed use. Screw size isn't particularly important at these weights, but maybe a #10 (5mm) or larger, length to suit the plywood thickness.
- Fingered joints. I own no clamps, so it would require buying them, I don't have jigsaw or router, so this would make me order cutting them on CNC. What's the required surface area to hold my load -- how many fingers would I need.
Do you have a table saw? Box joints can be fairly easy to make if you have one. Or you can invest the time and money in making a more complicated jig (this or this are examples).
I would recommend that the width of a finger of the box joint be no more than four times the thickness of the plywood. There isn't really a hard and fast rule for this: it's more of a gut feeling thing.
You don't necessarily need clamps to make boxes with box joints. Simple ratchet straps or even a rope turnbuckle can be used to clamp the box together.
If you have to go the CNC route, be prepared for it to cost you a pretty penny (unless you have access to the shop yourself).
- (Confirmat) screws through one board into the edge of another. -- How many do I need, do I need to drill holes for them? Should I worry that layers of plywood would come apart with time?
A butt joint with screws can have some issues with plywood. Even if you predrill the holes in the side grain of the plywood, you are still very likely to split the plies since the screw will act like a wedge between the layers.
You can reinforce the joint with glue, but don't expect it to last for a long time. I would advise against this type of joint.
One other thing you might want to consider is using a solid wood cleat on the inside of the corners to screw into. This will give the screws a better material to hold into and reinforce the corner from racking.
For this joint, I would use (6) screws per corner (3 per side), top, middle, and bottom. You'll have to stagger them slightly so that they don't overlap each other in the cleat. Again, #10 (5mm) screws will be fine, and length to suit the plywood and the cleat.