Are we salvageable?

Question

You wake up in a small room. The door is locked and there's no light other than 3 red glowing bulbs over a heavy iron door. Across the room you see a small table with a typewriter that doesn't seem to work anymore. You approach it and take a seat on a scruffy wodden stool, groaning deeply. Suddenly you feel your feet stumbling onto something soft and heavy below the table. You slowly get up again fearing the worst. You decide to have a short look, at least. Below the table there's a body wrapped up in pieces of cloth with its face turned towards the wall. A man about twice your age, his mouth still opened as if he was about to say something the moment he passed away. The little amount of light makes it almost impossible to see properly. In his right hand you find a small piece of paper...

8 ≠ 08

  d
8 13 4 8 10 // 10 07 8 8 0 // 09 16 5 09 0

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Hints:

• No image editing needed.
• No fancy tricks. Very simple mathematical operations are enough.

Answer 1

Solution (after some heavy hinting from the OP):

Here's how you decode the cipher:

You want to get three Imgur links to three images of green lamps. Each $5$ number group corresponds to one URL. Start from the original red lamp image URL ($pqvZn$), convert it to numeral ($a=1\dots$), add the numbers of each cipher and convert it back to letters (mod $26$) preserving the original capitalization (for example for the first one you get $xdzHx$) and then change the capitalization of each letter that doesn't correspond to a double digit number ($07$ is considered a double digit number and that's what the hint $8\neq 08$ is supposed to mean).

My opinion on the puzzle:

This puzzle looked like it was well crafted, but the cipher is really bad. A good cipher should be capable of encoding any type of message and this one can't. For example you if one of the solutions had a $D$ as a second letter you wouldn't be able to encode it with this cipher because writing $13$ doesn't change the capitalization. All you can get $q\to d$.

Old (and wrong) line of reasoning:

Start from the Red to Green image. I think this means what to open the door we need to turn those red light into green ones. How do we do this? By decrypting the message on the bottom on the paper. You can see that it is made by $15$ numbers divided into $3$ group of $5$ numbers. Also you can note (thanks @GarethMcCaughan)the string "pqv" that is the first three letters of the Imgur link of the red lights. Putting this all together makes me think that the solutions will be made of three Imgur link of three images of green lights that you get by assigning a value to each number of the code.

Each Imgur link is made of 5 characters that can be letters $a,\,\dots,\,z,\,A,\,\dots,\,Z$ or numbers $0,\,\dots,9$. Here is where I think the clue $8\neq 08$ fits. I think that $8$ means "this is an encoded letter" and "$08$" means "this is the number $8$ on the URL". This means that so far we got the three images:

- xxxxx.jpg
- x7xxx.jpg
- 9xx9x.jpg

Now, how do you decode the letters then? Since my hypothesis is that you need to change the red lights into the green ones I think you should start from the original image URL and change those letters by subtracting the cypher number from its value (a=1, b=2, ...). This might be confirmed by the $d$ over the number $13$. The original URL is pqvZn. If you take the second letter $q$ and you subtract $13$ you get $d$. Since all the three red lamp images are the same you need to start from the same URL in all the three cases.
If you do this for all the numbers here's what you get:
- hdrrd.jpg
- f7nrn.jpg
- 9aq9n.jpg

But none of those images actually exists. As you can see I'm obviously missing the capitalization of the letters. I don't know whether a letter will be lowercase or uppercase. If I preserve the capitalization of the original URL (so only the 4th letter will be uppercase) I still get nothing.

Answer 2

Based off of FrodCube's answer I am going through the iterations of possible images, I will edit this as I find more. My guess is that this is pure coincidence that this exists:

https://i.stack.imgur.com/hDrRd.jpg
the other strings given by FrodCube do not have existing images associated with them.