Continuously Adjust Element Size as Screen Size Changes

Resize constantly-changing image to fit size-changing screen, using CSS

I think this layout structure hits all of your requirements. There are three images of varying size in here I took the opacity down so you can see how they all scale together.

<!DOCTYPE html>
<html lang="en">
<head>
    <meta charset="UTF-8">
    <meta name="viewport" content="width=device-width, initial-scale=1.0">
    <title>Document</title>

    <style>

        body {
            margin: 0;
        }

        .images {
            position: relative;
            height: 100%;
        }
    .image {
        position: absolute; 

        background-size: contain;
        background-repeat: no-repeat;
        background-position: center center;

        width: 100%;
        height: 100%;

        opacity: 0.5;

    }
    .image-container {
        position: relative;
        width: 100%;
        height: 100%;
    }
.container {
    display: flex;
    flex-direction: column;
    height: 100vh;
}

.footer {
    background-color: black;
    color: white;
    height: 50px;
    width: 100%;
    margin-top: auto;
}
    </style>
</head>
<body>
    <div class="container">
        <div class="images">
            <div class="image-container">
                <div class="image" style="background-image: url(https://unsplash.it/1000/425)"></div>
                <div class="image" style="background-image: url(https://unsplash.it/640/1000)"></div>
                <div class="image" style="background-image: url(https://unsplash.it/800/800)"></div>
            </div>
        </div>
        <div class="footer">Content</div>
    </div>
</body>
</html>

How to auto adjust the div size for all mobile / tablet display formats?

This is called Responsive Web Development(RWD).
To make page responsive to all device we need to use some basic fundamental such as:-

1. Set the viewport meta tag in head:

<meta name="viewport" content="width=device-width,height=device-height,initial-scale=1.0"/>

2.Use media queries.

Example:-

/* Smartphones (portrait and landscape) ----------- */
@media only screen 
and (min-device-width : 320px) 
and (max-device-width : 480px) {
/* Styles */
}

/* Smartphones (landscape) ----------- */
@media only screen 
and (min-width : 321px) {
/* Styles */
}

/* Smartphones (portrait) ----------- */
@media only screen 
and (max-width : 320px) {
/* Styles */
}

/* iPads (portrait and landscape) ----------- */
@media only screen 
and (min-device-width : 768px) 
and (max-device-width : 1024px) {
/* Styles */
}

/* iPads (landscape) ----------- */
@media only screen 
and (min-device-width : 768px) 
and (max-device-width : 1024px) 
and (orientation : landscape) {
/* Styles */
}

/* iPads (portrait) ----------- */
@media only screen 
and (min-device-width : 768px) 
and (max-device-width : 1024px) 
and (orientation : portrait) {
/* Styles */
}

/* Desktops and laptops ----------- */
@media only screen 
and (min-width : 1224px) {
/* Styles */
}

/* Large screens ----------- */
@media only screen 
and (min-width : 1824px) {
/* Styles */
}

/* iPhone 4 ----------- */
@media
only screen and (-webkit-min-device-pixel-ratio : 1.5),
only screen and (min-device-pixel-ratio : 1.5) {
/* Styles */
}

3. Or we can directly use RWD framework:-

Bootstrap
Foundation 3 etc.

Some of good Article

Media Queries for Standard Devices - BY CHRIS COYIER

CSS Media Dimensions

4. Larger Device, Medium Devices & Small Devices media queries. (Work in my Scenarios.)

Below media queries for generic Device type: - Larger Device, Medium Devices & Small Devices.
This is just basic media types which work for all of scenario & easy to handle code instead of using various media queries just need to care of three media type.

/*###Desktops, big landscape tablets and laptops(Large, Extra large)####*/
@media screen and (min-width: 1024px){
/*Style*/
}

/*###Tablet(medium)###*/
@media screen and (min-width : 768px) and (max-width : 1023px){
/*Style*/
}

/*### Smartphones (portrait and landscape)(small)### */
@media screen and (min-width : 0px) and (max-width : 767px){
/*Style*/
}

How to keep a div constant in size as the user zooms in and out on the page?

There is no good way (read: reliable) to do this. Sorry.

What you're asking for basically boils down to detecting the zoom level of the browser, and there's a great answer here (confirming just how difficult this is):

How to detect page zoom level in all modern browsers?

As stated in that answer, there is a "kinda" cross-browser crazy way involving the use of Flash, but there are downsides:

It uses Flash.
It's not reliable if the user loads your page already zoomed in.
It uses Flash. Yes, this is so bad that I said it twice. Think of all those iPhones/iPads.

Anyway, it's here:

http://blog.sebastian-martens.de/2009/12/how-to-detect-the-browser-zoom-level-change-browser-zoo/

Detecting real time window size changes in Angular 4

To get it on init

public innerWidth: any;
ngOnInit() {
    this.innerWidth = window.innerWidth;
}

If you wanna keep it updated on resize:

@HostListener('window:resize', ['$event'])
onResize(event) {
  this.innerWidth = window.innerWidth;
}

Making a div appear at the same position regardless of screen size

Use vw (viewport width) instead of percentage. 1vw = 1/100th of the viewport width - regardless of device PPI, etc.
So, if you want the div to remain proportionally fixed regardless of device size and scren resolution - set your horizontal axis position with VW.

Example:

.somediv{ margin-right:20vw}