Is there any way to possilbly download only rides/shops/paths for the LOTR Project without all of the scenery?

What I would suggest doing is to go ahead and download everything, but instead of unzipping it directly into your objidata file, unzip it into a new file...title it RCTLOTR or something. Then use the RCTExplorer to go through and see what you want to use, copy and paste your selections into your objidata file. Then save everything else in the LOTR file in case you might want it later.

I've done this myself with many large packs.

I downloaded the scenarios, but do I have to open the in RCT2 to find out what i want and don't want?

Yes, in order to get the items that were exported with the scenario, you do need to open it in the game...I'm not sure if they are available just as a zip file, for the majority of people they find it easier to download everything at once included in a scenario. You could certainly still use the RCTExplorer to look for things to remove from your objidata folder afterwards...

Unfortunately with 1000 total DATs in the LOTR Project alone it would be impossible for us to go through and sort/organize them into separate downloads/zips by style, shops, etc. at this time.

I don't use RCTExplorer much, but DAT Checker works well, too. To make it easier for you to find the objects in your /ObjData/ folder, however, they all should start with "LOTR" at the beginning of the DAT name (i.e. LOTRxxxx.dat).