I just picked one of these units up and am having the same problem with the crackling, along with another 388 user. You may want to keep an eye on
this thread . I plan to give the unit a good cleaning this weekend and will update with any progress I make on that issue.
The fading in and out on the recording could be a number of things. I had a exact same problem (but on different tracks) when I first tried the machine and it came down to the tape I was using was simply too old. As well, I was informed that there were a number of years, around '76 I believe, that tape was manufactured with a bond that left an abnormal amount of residue on the heads.
Any sort of build up on the heads could 'cause this, so I'd suggest giving them a good clean. Magnetized heads can degrade the quality of the recording/playback, as well as the tape itself, but being new to the analog game I'm not sure to what extent (from what I understand it's usually over the long term and you will usually notice it in the high end; theoretically there could be enough magnetic buildup to completely erase sections??). I'd imagine this is probably not the case or the recording would probably degrade with every playback, but either way you probably should look at getting that done.
As far as DBX goes, what level are you recording at? I found that if I kept the levels just below the 0 mark instead of between 0 and 3 as the manual suggests, it sounded great, but above that it seems to start to drop out in the louder parts with DBX on. Keep in mind that the DBX on this system is not the greatest, even at the time it was released. Just like any noise reduction, some things work really well with it, some don't. I found that bass and drums really benefit from this DBX, yet something that requires a bit more detail gets a bit compressed sounding... but then it sounds like you have used this unit before, so you probably know what the DBX should sound like, it may just be cooked.