it's quite unstable, so I place it on a base, smth like 1'x20'x32'. Is it too wide
I hope you mean 1" x 20" x 32" :-)
The solution is to fix the shelving unit to the wall. Use a metal bracket or drill through the back panel and reinforce that part of the panel if needed. It doesn't matter that the overall weight is supported on the floor. Tall thin items must be firmly secured to the wall at or near the top to prevent them tipping over and killing a climbing visiting niece etc.
I ty to connect the parts and it's a disaster. Meaning that when I place two shelves together, they don't align in any sense.
One solution is to sketch the design in advance. Include actual thickness of boards in your design (don't treat boards as two-dimensional objects). That way you can work out shelf alignment exactly. Measure and mark shelf positions on each board prior to assembly and either transfer marks from one board to an aligned adjacent board or compare them this way afterwards.
There exist "shelf support template OR jig" products to aid in precise alignment of shelf supports in shelving units.
but except to Billy shelves from IKEA, I didn't find anything interesting close enough to what I need.
I have an unused IKEA purpose-designed CD/DVD shelf-unit in my garage gathering dust and cobwebs. It wasn't Billy though, it was GNEDBY
For wider units, you could buy several and join them while discarding one of each surplus interior doubled uprights (i.e. make an IKEA hack) - drill through the existing holes to make shelf-support points on both sides of the interior uprights.
Or buy just one GNEDBY and replace the narrow back-panel and shelves with wider boards.
You still need to fix it to the wall.