Can photoshop randomly distribute a bunch of photos and text if they're all on separate layers?

If it should be necessary to avoid rotated Layers to extend beyond the Canvas’ edges it would be possible to split the rotation and the moving into two operations, so that the Bounding Box resulting from the rotation is known before moving. 

This might cause problems with Adjustment Layers, but in your example there don’t seem to be any. 

// randomly place layers;
// 2023, use it at your own risk;
if (app.documents.length > 0) {
var originalRulerUnits = app.preferences.rulerUnits;
app.preferences.rulerUnits = Units.PIXELS;
var myDocument = activeDocument;
var theLayers = collectLayersBounds ();
var docWidth = myDocument.width;
var docHeight = myDocument.height;
var docCenter = [docWidth/2, docHeight/2];
for (var m = 0; m < theLayers.length; m++) {
var thisOne = theLayers[m];
var theId = duplicateMoveRotateScale (false, theLayers[m][1], Math.random()*(docWidth-thisOne[3])-thisOne[5][0]+thisOne[3]/2, Math.random()*(docHeight-thisOne[4])-thisOne[5][1]+thisOne[4]/2, 100, 100, Math.random()*360)
theLayers[m][1] = theId;
};
app.preferences.rulerUnits = originalRulerUnits;
};
////// collect layers //////
function collectLayersBounds () {
// get number of layers;
var ref = new ActionReference();
ref.putEnumerated( charIDToTypeID("Dcmn"), charIDToTypeID("Ordn"), charIDToTypeID("Trgt") ); 
var applicationDesc = executeActionGet(ref);
var theNumber = applicationDesc.getInteger(stringIDToTypeID("numberOfLayers"));
// process the layers;
var theLayers = new Array;
for (var m = 0; m <= theNumber; m++) {
try {
var ref = new ActionReference();
ref.putIndex( charIDToTypeID( "Lyr " ), m);
var layerDesc = executeActionGet(ref);
var layerSet = typeIDToStringID(layerDesc.getEnumerationValue(stringIDToTypeID("layerSection")));
var isBackground = layerDesc.getBoolean(stringIDToTypeID("background"));
// if group collect values;
if (layerSet != "layerSectionEnd" && layerSet != "layerSectionStart" && isBackground != true) {
var theName = layerDesc.getString(stringIDToTypeID('name'));
var theID = layerDesc.getInteger(stringIDToTypeID('layerID'));
var theBounds = layerDesc.getObjectValue(stringIDToTypeID("bounds"));
var theseBounds = [theBounds.getUnitDoubleValue(stringIDToTypeID("left")), theBounds.getUnitDoubleValue(stringIDToTypeID("top")), theBounds.getUnitDoubleValue(stringIDToTypeID("right")), theBounds.getUnitDoubleValue(stringIDToTypeID("bottom"))];
var theWidth = theseBounds[2] - theseBounds[0];
var theHeight = theseBounds[3] - theseBounds[1];
var theCenter = [theseBounds[0]+theWidth/2, theseBounds[1]+theHeight/2];
theLayers.push([theName, theID, theseBounds, theWidth, theHeight, theCenter])
};
}
catch (e) {};
};
return theLayers
};
////// duplicate layer and move, rotate and scale it //////
function duplicateMoveRotateScale (copyOrNot, theID, theX, theY, theScaleX, theScaleY, theRotation) {
selectLayerByID(theID,false);
smartify (activeDocument.activeLayer);
var ref = new ActionReference();
ref.putProperty (stringIDToTypeID ("property"), charIDToTypeID ("LyrI"));
ref.putEnumerated(charIDToTypeID("Lyr "), charIDToTypeID("Ordn"), charIDToTypeID("Trgt")); 
d = executeActionGet(ref); 
var theID = d.getInteger(charIDToTypeID('LyrI')); 
try{
var idTrnf = charIDToTypeID( "Trnf" );
    var desc10 = new ActionDescriptor();
    var idnull = charIDToTypeID( "null" );
        var ref6 = new ActionReference();
        ref6.putIdentifier( charIDToTypeID( "Lyr " ), theID );
/*        ref6.putEnumerated( charIDToTypeID( "Lyr " ), charIDToTypeID( "Ordn" ), charIDToTypeID( "Trgt" ) );*/
    desc10.putReference( idnull, ref6 );
    var idFTcs = charIDToTypeID( "FTcs" );
    var idQCSt = charIDToTypeID( "QCSt" );
    var idQcsa = charIDToTypeID( "Qcsa" );
    desc10.putEnumerated( idFTcs, idQCSt, idQcsa );
    var idOfst = charIDToTypeID( "Ofst" );
        var desc11 = new ActionDescriptor();
        var idHrzn = charIDToTypeID( "Hrzn" );
        var idPxl = charIDToTypeID( "#Pxl" );
        desc11.putUnitDouble( idHrzn, idPxl, theX );
        var idVrtc = charIDToTypeID( "Vrtc" );
        var idPxl = charIDToTypeID( "#Pxl" );
        desc11.putUnitDouble( idVrtc, idPxl, theY );
    var idOfst = charIDToTypeID( "Ofst" );
    desc10.putObject( idOfst, idOfst, desc11 );
    var idWdth = charIDToTypeID( "Wdth" );
    var idPrc = charIDToTypeID( "#Prc" );
    desc10.putUnitDouble( idWdth, idPrc, theScaleX );
    var idHght = charIDToTypeID( "Hght" );
    var idPrc = charIDToTypeID( "#Prc" );
    desc10.putUnitDouble( idHght, idPrc, theScaleY );
    var idAngl = charIDToTypeID( "Angl" );
    var idAng = charIDToTypeID( "#Ang" );
    desc10.putUnitDouble( idAngl, idAng, theRotation );
    var idIntr = charIDToTypeID( "Intr" );
    var idIntp = charIDToTypeID( "Intp" );
    var idbicubicAutomatic = stringIDToTypeID( "bicubicAutomatic" );
    desc10.putEnumerated( idIntr, idIntp, idbicubicAutomatic );
    var idCpy = charIDToTypeID( "Cpy " );
    desc10.putBoolean( idCpy, copyOrNot );
executeAction( idTrnf, desc10, DialogModes.NO );
//var thisCopy = app.activeDocument.activeLayer;
return theID
} catch (e) {}
};
////// function to smartify if not //////
function smartify (theLayer) {
// make layers smart objects if they are not already;
if (theLayer.kind != LayerKind.SMARTOBJECT) {
    activeDocument.activeLayer = theLayer;
    var id557 = charIDToTypeID( "slct" );
    var desc108 = new ActionDescriptor();
    var id558 = charIDToTypeID( "null" );
    var ref77 = new ActionReference();
    var id559 = charIDToTypeID( "Mn  " );
    var id560 = charIDToTypeID( "MnIt" );
    var id561 = stringIDToTypeID( "newPlacedLayer" );
    ref77.putEnumerated( id559, id560, id561 );
    desc108.putReference( id558, ref77 );
    executeAction( id557, desc108, DialogModes.NO );
    return activeDocument.activeLayer
    };
return theLayer
};
// based on code by mike hale, via paul riggott;
function selectLayerByID(id,add){ 
	add = undefined ? add = false:add 
	var ref = new ActionReference();
		ref.putIdentifier(charIDToTypeID("Lyr "), id);
		var desc = new ActionDescriptor();
		desc.putReference(charIDToTypeID("null"), ref );
		   if(add) desc.putEnumerated( stringIDToTypeID( "selectionModifier" ), stringIDToTypeID( "selectionModifierType" ), stringIDToTypeID( "addToSelection" ) ); 
		  desc.putBoolean( charIDToTypeID( "MkVs" ), false ); 
	   try{
		executeAction(charIDToTypeID("slct"), desc, DialogModes.NO );
	}catch(e){
	alert(e.message); 
	}
};

Could you please post screenshots with the pertinent Panels (Toolbar, Layers, Options Bar, …) visible? 

If the Layers with name and date should stick with the Layer with the image how can they unequivocally be collated? 

Would you consider building this project in InDesign or must it be in Photoshop?

For a start, you can try these:

https://community.adobe.com/t5/photoshop-ecosystem-discussions/help-need-edit-script-layer-shuffle/td-p/10764833

https://community.adobe.com/t5/photoshop-ecosystem-discussions/shuffle-selected-layers-only/m-p/9249453

https://www.reddit.com/r/photoshop/comments/5kajgh/how_to_shuffle_layers/

Info on saving and using scripts:

https://prepression.blogspot.com/2017/11/downloading-and-installing-adobe-scripts.html

Can you post screenshot with some examples?
If I can understand what you want to do then only script can help you. I will tag few scripters @c.pfaffenbichler @Stephen Marsh @r-bin @jazz-y