Is it possible to disable full backups completely, and if so do I need to run a full backup first, or can I just start from 0 and add folders as needed? Are there any downsides to running incremental only?
Ideally I would like a CrashPlan-style setup, where new files are added to the pile and no full backups occur. Images would take up too much space and this is a small setup, I’m not bothered about reinstalls.
Yes you can deactivate Full File Backups but this is nonesense.
If you run incremental images you need a base full image. Then you’d have to decide if the increments should be always based on that full image, or rather be based on the previous increment. (we chose the second option)
After that you “could” run only increments. BUT you cant delete increments because if one increment is missing all Data after that are broken. (option2 - in option1 the increments would get huge after a while) Even if no increment ever breaks, you cant delete them! So, after a year or two, you gathered tons and tons of Data garbage.
The Best Practice for this is to run a Rotation. For example like this:
FULL-inc-inc-inc-FULL-inc-inc-inc
after the last inc, there will be another FULL and if the full succeeded the first “FULL-inc-inc-inc” Block will be deleted.
That way you’d have (if you run it daily) a two Week Versioning with a “failover” dataset (if one Block is broken because of a damaged or missing inc, you have the other). [If you run it only once a week you’d cover 8 Weeks - for example]
Ideally you’d use a filesystem with deduplication or the offline dedupe from the MS Server 2012R2 (works like a charm, we have that running).
if you just want to “copy all that stuff in a folder to have it somewhere else and just piling it up” you could do this with robocopy in Windows (roll it out as a bootscript or something) or rsync in Linux.
Anyway you can add new folders anytime and they’ll just be added to the backup.
TL;DR
yes, its possible - but absolutely not recommended.
Okay, now I need to correct this 
You can run only incrementals. If you have Internet clients the default is to only run incrementals. There are different ways to achieve this if you have local clients. One of them is to increase the full file backup interval to something large. You can also set the minimal number of full file backups to zero so they get deleted at some point, or you can manually delete them on the web interface after the client has a incremental file backup.
With btrfs or ZFS you can also do “incremental forever” image backups. The only point where incremental backups depend on the last full is with image backups to VHD files and even there it is able to do synthetic full image backups, so it does not have to transfer the data again.
It turns out each incremental file backup contains as full? since you say that the full can be disabled and it will later be removed by the server?