I can tell you the answer for the second question: How to show UTM-coordinates in the lower right corner.
In leaflet the internal coordinate system is always longitude/latitude as far as I know, and you have to transform every time you need to work with your data.
First make sure you have installed proj4.js and proj4leaflet.js. To show your coordinates you can use the plugin: https://github.com/ardhi/Leaflet.MousePosition .
Then define your coordinate system and use when you define your map object:
var crs = new L.Proj.CRS.TMS('EPSG:25832',
'+proj=utm +zone=32 +ellps=GRS80 +units=m +no_defs',
[120000, 5900000, 1000000, 6500000],
{resolutions: [1638.4, 819.2, 0.1]
});
var map = new L.Map('map', {
crs: crs,
continuousWorld: true,
worldCopyJump: false
});
The function _onMouseMove() should be modified to something like this:
_onMouseMove: function (e) {
var my_crs = map.options.crs; // get the coordinate system
var my_proj = my_crs.projection; // get the projection, which makes the transform
var my_point = my_proj.project(e.latlng); // Here we transform back to UTM
var lng = my_point.x;
var lat = my_point.y;
var value = this.options.lngFirst ? lng + this.options.separator + lat : lat + this.options.separator + lng;
var prefixAndValue = this.options.prefix + ' ' + value;
this._container.innerHTML = prefixAndValue;
}
You will then get your mouse position in UTM. For more information see the documentation for proj4leaflet and leaflet.mouseposition.