Whenever it comes to automation, first thing coming to mind is Tasker: over at Android.SE we sometimes think this app is the answer to every second question. I'm a Tasker user myself, so I can say from my own experience it's a very powerful tool.
I'm not using it for anything like what you've defined, but from the features available I know it's capable of this. You'll have to invest some time to build a corresponding profile, but I'll give you a raw idea/concept here. Tasker executes "tasks" on "conditions", so you can think of it as "whenever [condition] is met, [task] will be executed". So let's go for a "pseudo-code" example:
- WiFi connected (parameter: your WiFi's SSID)
- File exists (your input file)
- Change to target directory
- Read the file line by line. For each $line: HTTP_GET $line
- Delete/rename (your input file – to avoid it being processed in an endless loop)
How it meets your requirements:
- Should be able to receive links somehow beforehand: Yes
- Should download files only over WiFi, not 3g/gprs: Yes (configurable, so you also could do it the other way around ;)
- Should work on android 4.0+: Yes (I use it a.o. on 4.0)
- Should be able to accept links in a bunch, preferably in text format: Yes, can process a file line-by-line as outlined
- Should not have limit on number of links: I'm not aware of any. Though size of the input file might matter :)
- Preference to free app: Unfortunately not. But there's a free 7-day trial available on their homepage. Trial period can be extended in 7-day-intervals with a trick, though: Export the configuration, uninstall the app, re-install the app, import configuration (this hint comes from the developer himself, so I freely mention it here).
To give you some visual, here are some screenshots:
Some screenshots to demonstrate the powers of Tasker (source: Google Play; click images for larger variants)
Tasker can be very complex, though – that comes with its powers. To lookup its possibilities, there's a User Guide available. The Tasker Wiki also has useful resources, like a walk-through to get a first feeling, or example profiles created by other users.