Lots of questions...
First of all I would use this path:
C:\Program Files\Firaxis Games\Sid Meier's Civilization 4\Beyond the Sword\Mods
I think I read that the other path can work, too, but I never tried it out myself. A would also guess that the second path is for temporary files which may be a reason why it can cause problems if you use it instead of path 1.
Generally spoken it is possible that all you have to do to install a mod is downloading its files (usually an archive like rar, zip or 7z), to copy / extract the mod to path 1 you have mentioned, start the game, select "advanced" and then "load a mod" and then select your mod. It is also possible to combine mods without any additional work. Usually you will have to spend a little more time. First of all you should know that a structure of a complete modular mod has a single folder in path 1, the name may be MODNAME. In MODNAME there is an Assets folder that consists of a Modules folder which has at least one folder named after a civilization or a nation. What a difficult sentence, I hope you will get what I mean. Some modders only upload the folder that belongs into Modules, others, like me, provide the full structure. You will have to check first what kind of mod you have loaded and depending on the type of the mod you'll have to create some additional folders. In the case that the mods file structure is incomplete, you will also have to edit / create some config files. You should load your mod over the menus as described above. Your mod won't work now. Leave the game, go to path 1 and open your mods mainfolder. There should be an ini now that have been automatically created by loading the mod once. Open it and search for the line ModularLoading = 0, change it to ModularLoading = 1. This step is not needed if the file structure is complete. The next thing might not be necessary to do, on my laptop it wasn't necessary but on my desktop pc it was, maybe it depends on which patches you have installed. Search in C:\Program Files\Firaxis Games\Sid Meier's Civilization 4\Beyond the Sword\ for a file called _Civ4Config (it is a link, so you may see .lnk at the end) and open it. Search again for ModularLoading = 0 and change it to ModularLoading = 0. Theoretically you could now take different subdirectories of Modules from different mods and copy them in your mods Modules. For a lot of mods that should work. On the other hand you should also know that not all features a mod could use (for example a unique unit select / order sound) can be made modular. My Magyar mod for example adds Hungary with UU, UB, leaders and unique unit artstyle (all modular) and uses an unique artstyle for buildings (different building graphics for Hungary) and hungarian unit select / order sound (the last two are non-modular). So my mod is mixed. In this case you still could copy the subdirectory of my mods Modules to yours, but this is not enough. You will also have to copy the non-modular parts that are represented by folders in Assets (except of Modules of course). If you have two mods to combine that both use non-modular parts, for example my Magyar mod and my Hun mod, it isn't enough to simply copy everything from Asserts together. The reason is that there would be same files in different versions used by both mods, for example the file that tells the game where to look for sound files. In this case you would have to open the files and copy only the parts one mod added to the other file. For example you would copy the xml entries the Hun mod adds to the sound file into the same file of my Magyar mod which you would have to entirely copy into your mods file structure. Because there are different things that can be added non-modular no detailed manual about how to do that can be given here. Usually you will know if a mod is mixed or modular only if you look at his description on the forum. If it adds unit order / select sounds you will know it is not entirely modular (although there are ways to make them modular AFAIK, but this not a BtS standard again, which means you will have to do something additional not here described).
Now about starting a mod automatically with BtS. This actually doesn't have anything to do with modular or non-modular. By default you will have to load any mod separately over the menus, but there are ways to force the game to do what you want it to. AFAIK there is a way to integerate a mods files to the game, but I strongly dislike it, because you could damage your installation of BtS by overwriting something. I never tried it out by myself, so I can't tell you how to do it. Another, more cleaner and secure way is to change the properties of the shortcut you are using to start BtS. So right click on that shortcut, it doesn't make a difference whether the shortcut is on the desktop r in the start menu, and select properties. The first editable field on the following window should contain:
C:\Program Files\Firaxis Games\Sid Meier's Civilization 4\Beyond the Sword\Civ4BeyondSword.exe
change it to
C:\Program Files\Firaxis Games\Sid Meier's Civilization 4\Beyond the Sword\Civ4BeyondSword.exe -mod="Mods\MODNAME"
Note that MODNAME is the name of the Mod you'd like to load automatically. To look up the exact name of your mod, just look what the mods folders name is in path 1.
I hope this helps you to find an answer to you question.
