I believe I am failing to grasp your main problem. Are you limited by the surface area of land available to make your pond?

Your dam height will be measured from the pre-construction land elevation at the mid-line of the dam to the post-construction top of the dam.

However, you can excavate as deeply as you want in front of the dam. That is not typically considered part of the "dam height". You could dig 10m deep in front of the dam. If your dam breaks catastrophically, you are not sending a wall of water 10m high into your neighbor's property. It would always be no greater than the height of your dam above the ground surface.

IMO, you need to design your full pool water elevation and then add some freeboard to your dam height ABOVE that level. Never let a heavy rain allow the water flow in your little valley to rise over the top of your dam. It will quickly cut out your dam.

You need an outlet pipe and/or a surface spillway to protect your dam and pass through excess water.

Once you have your design elevation for the water level, you just need to excavate the pond area, side slopes, and bottom contours to create your desired pond. I expect you will have excess soil available if you create your water depth to 3 meters. You can spoil this around the pond to make attractive landscaping or just turn your straight dam into a "U" shape.

As to your dimensional questions:

For most embankment dams, the front slope and rear slope should NOT be greater than 3:1. Typically if you have a significant amount of non-cohesive material in the fill (such as sand, gravel, or rocky debris), then the downstream slope should be further reduced to about 2:1.

Further, my guide says 6' of minimum top width for a dam of up to 10' in height. Use a minimum of 8' for the top for a dam of up to 14' in height. (I apologize for switching the units out of meters.)

However, for the small dimensions of your swimming pond you may be able to conceive of the project differently. Imagine you are digging a hole with a volume of 150 cubic meters. You are then landscaping your beach/view/yard to place up to 195 cubic meters of spoils. (There may be a fluff factor as high as 20-30% for your excavated volume after it is spread and compacted into place as your spoils volume.)

A pond that is up to 10' deep can probably be sealed with a clay blanket of 12" minimum thickness in all dimensions. The blanket must be constructed by using sub-soil material with the proper clay content, and moistened and compacted in lifts of 6" or less.

The exception would be your "dam" to the down slope side of the valley. Even being "sealed", it must have the mass to resist the pushing force of your impounded water. However, I think you could do that only 3-4 feet above grade. (Assuming I am understanding your project correctly.)

Finally, another affordable option for a pond that size would be to use a pond liner. You could have nearly vertical sides to a depth of 3m in the places the big kids are jumping and diving. You could then build a very gentle slope on the other side and cover the liner with sand to make a walk-in beach for the smaller kids.

Hopefully you can translate my gibberish into some useful ideas for the guy that actually has eyeballs on the project.

Good luck on your new pond!