First of all make shure your X SP is fully charged and you are using a working USB OTG cable adapter (preferably tested on other devices).
1. USB pendrives, SD and microSD adapters. Xperia SP supports out of the box USB storage meaning pendrives and SD adapters like Sandisk Cruzer (some old 4GBmodel) and some Sandisk 32 GB microSD car in Sony Ericsson's IM 920 adapter. All of them formatted as FAT32.
Yes I've encountered fails but related exclusively to voltage (both pendrives and SD adapters). Dunno which will work for you, better try before you buy.
2. Yes it supports exFAT. FWs prior to ...2.254 do not. I've tested them all. I am specific to the aforementioned. exFAt meaning you can mount microSD cards 64+ gigs and virtually any filesizes, think of 8 GB .mkv files.
3. It hurts when it comes to HDDs. Before anything make sure your external HDD has also an external power supply. It means you have to see a wire leading to a wall socket which is being actually connected. Otherwise your phone or tablet will never be able to power by itself a HDD, be it 2.5 or 3.5 inch. Moving on, I found plugging in any externally powered HDD does nothing by itself.
In comes the trick. I own a Xperia LiveDock DK10 for the 2011 range. It's externally powered and also has an USB OTG input. It helped me before with each pendrive which didn't work by itself when plugged in the USB OTG cable alone. Powering the dock supplied the energy the setup was lacking.
Since the most of you will find the dock redundant or missing from stocks I am glad to inform you all that some USB hub that was lying around, branded Manhattan, with external power supply, did exactly that job.
Here are some examples:
Toshiba 500 GB HDD FAT32 file format, 2.5" form factor, IcyBox enclosure, separate power supply, plugged in the 1st port of a Manhattan USB Hub, power supply powered in, mini USB output plugged in USB OTG adapter in Sony Xperia SP, fully charged. Played 1080p mkvs smoothly.
1500 GB Seagate/Samsung, 2000 GB Hitachi NTFS formatted 3.5 HDDs in powered racks, externally powered Manhattan USB hub, USB OTG cable, Xperia SP rooted, installed Paragon exFAT, NTFS & HFS+ and Paragon USB plugin for Total Commander, full size drive fully accesible.
Also Sony Nex camera, 64GB exFAT SD card inside, connected only with USB OTG cable on Xperia SP - working.