I've played my guitar for about 4.5 years and I have never cleaned it after playing. Why does it never rust? My guitar and bass strings are rusted after one month. As far as I know, the stainless steel strings can rust, isn't that true?
Here's are the pictures of my guitar The strings are from the first purchase, and I have never replaced them until now.
All forms of iron eventually rust. Pure iron rusts very quickly and visibly, within days if not even hours. The best stainless steel can go decades before showing the first signs, but it too will eventually rust. Everything else falls somewhere in between, depending on how it has been manufactured. (And in principle, the longer you want your metal to be rust-free, the more elaborate and expensive is the processing)
Also keep in mind that rust (iron + oxygen) is just one of many types of metal corrosion (any metal + acid or other chemicals).
Stainless guitar strings that corrode very quickly, I reckon, must be pretty cheaply made and/or used in a highly damaging environment, i.e. long time spent in high humidity or near-wet conditions.
And in some cases, people with highly acidic sweat can also cause metal corrosion:
http://www.sciforums.com/threads/what-causes-my-corrosive-sweat-and-how-can-i-counteract-it.113487/
https://www.sciencedirect.com/science/article/pii/S0010938X72912425
Otherwise, average guitar strings in normal, average conditions, should easily last months if not years before showing any signs of corrosion -- just go into any big guitar shop, where some of the instruments will have been sitting there for months or even years, and check the strings: even if they're cheap first mount strings and have been sitting there for a year or two, they will usually be OK.
Stainless steel can rust, it just takes longer depending on the grade and environment.
To my eye, your strings seem to have corroded as they appear in another colour at some spots. It does not look the typical red, but rust comes in many colour. These corrosion spots might be a result of the strings coming in contact with other metal parts of different material, like the tuners or the bridge. I cannot see any corrosion in the first photo. It's a bit hard to see with these photos, though, so I am not sure. The effect, when different metals in contact with each other degrade faster than normally, is called galvanic corrosion.
Some strings have coating giving corrosion-resistant properties. Ernie Ball has a nice blog about the topic: Coated vs. Uncoated Guitar Strings: What are the differences?
I don't say that your strings have coating. Even grease from your fingers can protect your strings against corrosion. And if you play often, your fingers polish strings and remove rust. I had one of my guitars sitting in the storeroom some time and it had sensible and visible rust on its strings. I was too lazy to replace strings, so after some days of active playing the rust from the strings' upper sides was gone.
But even if your strings doesn't have rust on them, new strings probably sound much better than ones sitting in your instrument for years.
My view is if you buy a brand new guitar from a shop, they come with factory strings, I'd usually replace them, as they've could be hanging around for months/years on that guitar.
I must admit one of my Strats strings hasn't been replaced in 5 years since purchase, but I've only played it less than 100 practice sessions. I've clean the strings every 3-4 weeks with a simple wipe, maybe why they've kept in good condition.
I recommend you to replace them, your fretboard looks a bit dirty and needs a clean, for the sake of the longevity of your guitar.
