Loud hum is almost always a bad TDA2002 on the AR, especially if it hums without the game board plugged in. You can use a DMM set to AC mV to test the SPKR1 and 2 test points on the AR, with no game board plugged in, to see which TDA is generating the hum (though you probably should just replace both, if you're going to do one of them.)
For the sparking fuse, is the fuse the correct value? Sparking usually doesn't happen on the deflection board, but those two top fuses will just straight blow if one of the deflection amps on the board is bad, or the frame transistors are bad. My guess is you're getting a large inrush current, but the fuse is glowing, but not blowing(?) The fuses should be 2A fast (i.e., normal) blow, not slow-blow.
Test the 4 heatsinked transistors on the deflection board first (using a DMM), then all other small black transistors. You can check them in-circuit for most cases, though it is possible to have them go bad in ways that you can't see unless you remove them, but that's maybe 5% of the time. It helps if you have a known-working good board to compare to, but in your case maybe you can use the other bad board as at least a partial comparison.
Also test and/or just replace D608 and D708, as these frequently go bad, esp if they are the original glass ones. They are fairly close to the large hot power resistors, and take a lot of heat.
Also, test your frame transistors. (There is a technique for doing this quickly in my 6100 set-up guide, which you can use identically for b/w vector monitors.)
Also, do the mod where you bypass R100 and R101 with straight wires (see the FAQ), and replace Q500, 501, and 502, as these frequently cause issues, from being cooked next to R100.