Thank you for asking me this but I'll be honest: I almost never use the any emulator, but since I sometimes check it and understand a little I'll try to explain.
Is it possible to dump a .pkg DLC or Update file then extract them using a program like:
PSN PKG Decryptor & Extractor
and then just put the extracted files in the PPSSPP appropriate folder as it is said in the PPSSPP FAQ
Ok, since I already did this I can confirm that you can use the pkg decryptor to get the needed files for both the emulator and the real PSP, but you cannot update any games using iso_tool with the emulator, since it's a function that only the real PSP can do and the emulator will corrupt your game, also for install the DLC there are two ways which depends on the files, if you get my files they have a .txt file with the proper install path, but I'll give you examples:
Dissidia 012: you have to insert the folder with the right ID matching the game's into the PSP\GAMES\ folder, so into the emulator should be like mine ppsspp\memstick\PSP\GAME\
(Notice that this GAME folder is also used for updates, emulators, homebrews and PSX games, however not all of this is supported by the emulator)
Monster Hunter 3rd: in this case you will have a SAVEDATA folder with this ID ULJM05800QST, so for this one you will have to put into your SAVEDATA folder which should be PSP\SAVEDATA, so into the emulator should be like this: ppsspp\memstick\PSP\SAVEDATA
Q2: If it is necessary to have the extra files (again I think .edat), is there a way to generate them on a PC so that I wouldn't need a real PSP to use them on PPSSPP?
Well, I can't say for sure how those files have their own licences, I own a PS3 so I understand what you mean, but unlike the PS3 it does not generates any other file besides the DLC's, so there's no licence to get or activate, but there are a few DLCs which doesn't work because it's somehow encrypted, like Taiko no Tatsujin, Dynasty Warriors Strikeforce 2 (which does not work on the real PSP but it works with the emulator. So... the files are decrypted and simply works anywhere, just like that.
Q3: If I install more than one DLC, do I have to adjust the PARAM.PBP files somehow?
Nah, you won't need to do anything if you already get the files organized, well, if you use the decryptor you will have some time organizing the files and moving them all to ONE folder since when you use the nopaystation to download them you will get for example:
Disgaea 2 which you will download all the characters DLC individually.
When you decrypt each of them it will have a folder with:
But it can vary from game to game and they are very alike the PS3's files and folders. So, you won't need another PARAM.PBP, you will only use ONE of them and does not matter which one. For the remaining files (almost all of them are .EDAT) since it does not share the same name it should work just fine, and if you have to overwrite it and they are not the same file, then it will have issues.
If I install more than one DLC
I'll explain a little more about it, for installing all content for a single game, like mentioned above, you only need one folder like I explained, well, the OS won't let you have more of them anyway. But let's talk about the custom DLC, which can be those for Dissidia 012, Project Diva or whatever, the custom content uses the official ones, so you may need the official ones to be able to play, in which case you will overwrite the official (or maybe not) so... you cannot have every custom content at once if they share the same custom files which overwrites another file for another custom content. Again, everything explained in all my .txt files spread into those files.
If DLCs and Updates work differently, please clarify
More or less in fact, they may share the same folder ID, but they don't share the same files and the updates doesn't need to be decrypted (or do they if you get them from nopaystation, anyway, is there any update for PSP games on nopaystation?), but the update needs to decrypt the game EBOOT (or something like that) and that's the part which the emulator cannot do and you need the real PSP do to it, you can also get some games already updated, but I recommend to do it own your own and I'll tell you one case, which is the Bleach Heat the Soul 7, once you have it updated you will only have access to the battles, I mean, you will lose every single option and mode from the game, you will be forever trapped into a single battle mode.
And I think that's all, I cannot say much about the differences about the DLCs and Updates since the only differences on how they work is like that, oh, did I mention that you will have to have the files as long as you're playing? Well, that's obvious but be aware that if you update any game you will need have the update into that folder (GAME folder) or the game won't work, well at least with the games I've done it.
If you have any question, you know, just ask and I'll try to answer them.