Odd wiring problem. Novice renovating house
There is more to household wire colors than you think you know. That's pretty evident because you find a white on the hot unusual - it's not. It SHOULD be remarked with black or red (or some other color, but those are most common) tape since it's being used as a hot, but it's very common, because /2 cables are black/white/bare or green and /3 cables are red/black/white/bare or green - so in a cabled building other colors (such as your blue) are not common, and for a LONG time it was both normal and code-legal to run a "switch loop" where an old-fashioned switch had a /2 cable running to it, no neutral, and the white was hot. That's not current code, (due to "smart switches" that need a neutral) but you'll find it in almost every house from before that code change took effect.

Now, that blue wire on the neutral side is more of a potential/probable code violation, but if the setup works as wired, it should work as wired the same. Using white for hot is OK (with remarking) but neutrals are only supposed to be white or gray, and grounds are only supposed to be bare copper, green, or green with yellow stripes. Blue is one of the "hot colors" in the expanded universe that conduit and rolls of wire give you. The main question being, where does that blue wire go to or come from? (Since we cannot see that in your picture.)

Other than replicating what wires are connected to what terminals (and NOT, in my very biased opinion, replicating the use of backstab connections) the main gotcha that we cannot see in your pictures at present is whether the "tab" connecting the two halves of the receptacle is broken - this is normally only done on the hot side, and is typical in the case of a "half-switched" outlet (also typical in the case of a MWBC but this lacks several clues that would imply that case.)

If you have more wires than firmly screw-clamped connections on the outlet, you run a "pigtail" or short wire which is then used to connect multiple wires using a correctly sized wire-nut or other wire connector.