Will not start the fuel pump was not getting power?

The fuse #8 in the under-hood fuse box? Should have a 15amp fuse. What 7.5amp are you referring to? Fuse 6 is the 7.5amp fuse for the overhead lamps, (diagram 3).
I'm referring to Fuse #8 which was in the under-hood fuse box, it feeds the ECM relay, that was the fuse you said was blown, correct?

Find the radio code so we can disconnect the battery and do some testing. I will get back with you shortly.

Okay, so basically once the overhead lamp circuit started smoking and blew the fuse, did it not start after that? I'm just trying to determine if both these events happened at the same time. It sounds like someone put a 20amp fuse in a 7.5amp location because it probably kept burning out the 7.5 due to a short and adding the 20 amp allowed a lot more current to flow, hence the smoke, so it was most likely not a dead short to ground on the circuit, or it would have blown the 20amp fuse right away. So there must have been some resistance to ground for this all to happen. A corroded connector will do that, when some current can flow between pins in a connector that are close to each other, the corrosion is resistance between the two pins but current still flows over it.
This is how wires melt together if you have ever seen that. Any resistance in a circuit causes heat to built up.

Either way, the reason the fuse for the overhead lamp just pops when you install it is there is a direct short to ground somewhere on the circuit before the load (bulb). If it was smoking like that, there's probably wires melted together, so I would check wherever you saw the smoke coming from. You'll have to pull the covers off the ceiling lamp, take the bulb out and with a flashlight see what you can up above the ceiling where the wires run.

Battery voltage is low, that doesn't help. It should be at least 12.6v. But see what you have for voltage at the data link connector on pin 16, check it twice, once using pin 4 as ground and then pin 5 for ground.

We will have to assume whatever burned out fuse 8 might be a wire that is not always making contact somewhere, some wire that might be moving around when the vehicle was running.
Do you have another key to try, or have you tried yet? Like a grey valet key? And there are not metal objects on the key chain or near the ignition switch?

We need scan tool data to see if the ECM is not allowing starting due to a key issue itself, or if the ECM is unable to communicate correctly, the communications issue seems more likely with all the scan tool problems, but I think the ECMs in these vehicles are difficult to get to being in the middle of dash if I remember correctly, it might be accessible from the passenger side floor behind the center console panel.

DC volts, it should read battery voltage, I would get a charger or maintainer on the battery because when testing with the key on the battery is just going to keep dropping and its already too low.
Im going to show you where we are on the flow chart for a flashing Immobilizer lamp as well.

Up to step 25, where the engine doesn't start and immobilizer lamp flashing, Honda wants a scan tool hooked up (The HDS is the factory Honda scan tool) but an aftermarket one will do to check for ECM communication.
See what voltage reading you get on pins 7 and then 14 also. Pin 14 is supposed to go directly to the Immobilizer, and pin 7 is the K-Line which is used for scan tool communications to the modules, the K-Line should have a 12volt signal, although a meter is too slow to read the signal, I want to see if there's anything there at all.

You can use pins 4 or 5 for ground, I'm not sure what you will see with a meter and the key On, but I'd expect to see something. The issue here is we don't know if the ECM and Immob, are communicating to each other. A scan tool that can read all the modules in the vehicle, so a higher end scan tool, can go into the security system and ECM to see what the data PIDs are reading. And tell us if the ECM is inhibiting starting due to not seeing the key through the Immob. Other issue might be corrupt data packets on the network, still a communication issue though.

We can have you disconnect the immobilizer connector and the ECM connector E which is where the two communicate the code it needs to allow starting, and see if that wire is shorted to ground or has high resistance, the immobilizer is on the steering column under the Ign switch(diagram 5, 6) and the ECM is here(diagram1) and the ECM connector E pin 27 wire colors(diagrams 3, 4, 5 are all connector E).
Make sure the key is off when doing this. I didn't even ask if this is a key Fob or not, I assumed the lock smith had done everything correctly, but I'm not so sure now.