You are in the conduit wiring method.
The rules here are different.
most likely, the ground is the metal conduit itself. That's done!
it is normal to have wires pass through your box without stopping. Those wires are not usable by you, and should be disregarded. (White and red)
Neutral will not be provided in switch loops because it is easy to pull neutral if it is needed in the future.
Your assessment of the purpose of the three black wires is correct, though more likely the 2 blacks are the always-hot, and the 1 black is the switched hot to the lamp. There are 2 always-hot blacks because power goes onward to other outlets or points of service. The neutral you see is surely for that onward use of power.
Note that the switched lead doubles back in the same conduit. That is fine. I'm a little disappointed that the installer didn't any of the 6 other allowable colors for the switched hot, to distinguish it, or at least mark it with tape.
I gather you are not familiar with multi-wire branch circuits (MWBC). I don't know what the red is, but it's probably an MWBC. This means there will be 2 breakers you must shut off to deenergize both black and red, and if you don't get them both, you will get electric shocks when separating the neutral. They may already be handle-tied in the panel. They should be by modern Code. (if it's a double-stuff, let us know!)
Getting neutral
You do not have neutral in that box. That loop is not available to you and might as well not exist. Don't even think of trying to bite onto that somehow, if you're gonna do something that nasty, you might as well bootleg neutral off the metal chassis of the box.
To get neutral to that box, you will need to pull it. As it happens, there is already a "rope" in the conduit fit for pulling a new neutral, so this will be easy but will involve gasp material cost. The material is #12 THHN, THWN-2 or XHHW wire that is white. Your pick, solid or stranded. You will be pigtailing both ends, so stranded will work great.
You see the white looping through. Follow it in both directions to whichever other box it goes to. You may need to open up a lot of junction boxes, although it's a guess that one direction goes toward/to the light. You shove the white wire up the conduit about an inch, and see if it moves on the other end. Also, get a handle on how stiff it moves, you are interested in the direction with the easier pull. You are not interested in a location where the white wire "loops through" like it does here. It needs to terminate there. We are going to use that white wire to pull in a new white wire.
Now, you've identified the easiest pull. All breakers must be off, don't let the MWBC bite you. Now, unhook that white wire. Straighten it out and lay your new white wire alongside it at least 9" of distance, so they overlap, and tape them to each other with electrical tape the whole length of overlap. They mustn't separate! Use tape at the lead to make sure the front of the new wire doesn't present a hard corner, or it will snag going through.
Now push this into the pipe. I prefer to push than pull, honestly, but eventually you'll hit a snag and pulling will make it easier. It's less brute-force, and more teasing it through. Twisting the wire often also helps.
You finish when you have all 3 ends of the white wire sticking at least 7" past the surface of the wall (10" past the end of the conduit). It can now be snipped to that length. See why we couldn't use the white as-is?
Now, we talk about a fundamental rule of MWBC. You must be able to remove a device without interrupting the neutral. Now since I gather your smart switch will come with wire leads, forcing you to pigtail, you will need to double-pigtail the neutral here. That way you can remove the smart switch later without having to separate the two wall neutrals. So wire-nut the two wall neutrals to a short 6" piece of white wire. This shorty then gets pigtailed to the smart switch's neutral wire.
Presumably, the other box you just ran white from will also have been pigtailed already, if not, pigtail it.
The two blacks that were on the old switch together, get pigtailed to the (presumably black supply) wire of the smart switch.
The remaining black goes to the switched-hot lead of the smart switch.
DON'T try random stuff when you get stuck
Trying to replace actual knowledge with "throw things at the wall and see what sticks" is a fatal error when dealing with electrical equipment. Why? The entire strategy is based on stopping when you find "the" combination that works. Actually, many combinations will work and also kill you. The only way to avoid those is skill, so the right thing to do is pause, research and measure.
I'll grant you if you are only connecting to 3-way switches, you can't go too far wrong - but nonetheless, this habit is so dangerous in almost any other context, that I want to address it.
Position of wires on multiway switches is useless
I assume you're changing switches and receptacles for color or style. In that, the most common gotcha (other than broken-off tabs on receptacles) is assuming 3-way switch builders do you any favors by keeping screw positions consistent. "They do not" is the understatement of the year. The only useful indicator is screw color.
Related, electrical wiring is not very well color-coded, and multi-way switch circuits are worse than not color-coded at all. I for one mark wires obsessively, so the next person has a chance of understanding the circuit.
Probably easiest to just "do it the old fashioned way". Travelers are always in the same cable (and are never ground wires obviously). Switch 2 is no help at all. So we look at switch 1. Only two are in the same cable (I can't see, you can) -- gotcha! Those are the travelers. Now, knock wood, that cable is continuous to switch 2, in which the same 2 colors will be the travelers there. (If it stops anywhere intermediate, all bets are off, and this is why I mark wires). Buy a 5-pack of colored tape, and mark all travelers yellow. There is no need to distinguish travelers from each other.
Then, travelers go on the brass screws. The remaining wire goes on black.
Edit: Looking at your photos in switch box 1, it seems clear the travelers are white and red. Wrap them with yellow electrical tape. Most likely they are also white and red at switch 2 (that's not 100% sure but it's the thing to try first.)
The light should have 1 terminal hot
Lights are the ultimate load, and in mains electrical, most loads connect between hot and neutral (unless you dealing with North American 240V or in the Philippines where everything is that). Therefore there should only be "hot" on 1 terminal, not both.
Edit: If the right lamp wire is energized, then most likely the 3-way set is delivering power correctly (it may still be wired wrong for the switches to work as intended).
If power is present at the right, and still it doesn't light, then it's a) burned out bulb. b) burned out socket. Or c) the neutral wire has a problem. There'd be no reason for the latter to happen, given that you don't touch the neutral when replacing 3-way switches.
Your next test is to fit the light bulb and test the left socket. If the left socket suddenly reads "hot", that means there's something wrong with the neutral wire. Otherwise you have a bad lamp or socket.
To answer your questions directly:
- If all six wires are hot, you need to file a warranty claim on your 3-way switches! The only other possibility here is that your voltage tester is picking up phantom voltage.
- Both sides of the lamp should never be hot. If it is, and the bulb is in it, that indicates a broken neutral wire. That left side is surely neutral.
- Neutrals don't have fuses. Their only overload protection is being monogamous to one hot, which is fuse/breaker protected. MWBCs are engineered to allow 2 hots to share 1 neutral. All other sharing creates overloads.
- Neutrals should never be hot. Travelers are in pairs; one will be hot. Switched-hot will only be hot when the switch is on. Always-hot is I'll give you 3 guesses. Notice I haven't mentioned a color yet. That's because colors don't necessarily correspond to functions. This is why I wrap tape around wires: in my world, switched-hot is red or blue, travelers are yellow in pairs. Here is how your box looks in my world.
(the thin lines are just to make clear which wire is which; the meat of what I do is the band of yellow.) The purple dashed line is a "Chinese Wall" between the left side and right side switches. Because nothing crosses, nothing is allowed to cross. That is relevant if you put a smart switch on the left: it must not steal neutral from the right.
Best Answer
If there is another switch in or near this room that also controls the same light or device then you need a 3 way switch to replace the old switch not the 2 way you are using. If this is the case, then the black wire is probably the feed and the 2 reds are the travelers to the 2nd switch.