^^
I generally refer to this list for devices supporting DD-WRT:
http://www.dd-wrt.co.in/wiki/index.php/Supported_Devices#Supported_Devices
Though it's cumbersome to lookup this list against what's available in India. Routers with USB port have higher chances of supporting downloads with PC switched off, such as Asus N16.
Regarding restrictions: You are trying to compare protocols (P2P, FTP, etc.) with software (IDM etc). You can make any device to support protocols (p2p, http, etc.) but in order to support user interaction in the absence of a PC (master device), you need to have some sort of OS on that device. Some routers have minimalistic OS to host a GUI for download support. e.g., Asus N13 has its own OS and a software (Download Master) to handle downloading, in the absence of a PC.
Router has to stay up if one is downloading non-stop from internet. So, router manufacturers made it convenient for end users to include a download queue manager, on top of the router (or modem) functionality... and therefore PCs can be shut down once you set up the download queue.
There are dedicated torrent download devices which run software meant specifically for handling torrents (so, they'll have better download managers). Download Master from Asus has very less functionality (e.g., you can't choose specific files to download from a huge torrent). People flash their routers with DD-WRT which provides more functionality to an otherwise boring router (Asus N13). There are other routers with probably better download managers from Belkin, Buffalo, etc. Asus N13U ver B1 tops the list in India, maybe because it's the cheapest router that supports OOB downloading with PC switched off and also DD-WRT.
There are many other routers available in India that supports PC-off downloading but my knowledge is limited to only N13 and N16 from Asus. @
blr_p is the walking encyclopaedia of networking/routers on TE
. May be, he can provide a few more names.