I'm aware of the ability to use accented characters by holding down a key until they appear (ie. á ü etc.); however, I'm curious as to how, if possible, one might enter a code point in hexadecimal format or otherwise to output the corresponding character?
UniK - Unicode & navigation Keyboard extension seems to be the closest to a character map and it also functions as a keyboard extension. You actually have to type hexadecimal code points in this app.
There are applications in the App Store that display all of the characters allowed in the Unicode set that you can copy and paste into other applications like Mail and the like. Searching "unicode" in the App Store brings up a whole slew of them, both free and paid.
There is also Glyphboard (visit with your iOS device) that you can save as a bookmark on your iOS device for an easy interface to some of the more popular ones. This is very lightweight and changes every so often.
I wonder if you ever found a way to enter Unicode characters directly on the ipad?
It's 2017.09 and the closest I've found is the app Unichar. Can't enter (uni)codes directly, but it has 18 unicode pages avaible (in the paid version, 8 in the free version.) Interesting is that it installs as an app that you can open, but also has a keyboard with the same level of features as the app and similar interface
This is as close of an answer as I've found to the same question. It's odd apple resists users' interest for so long.
I have been looking for similar and the best third party app I've found for arbitrary unicode input is called UnicodeLab.
It allows you to input any unicode in decimal or hex, view it in multiple fonts, and copy it to the clipboard. You can also cycle through neighboring character codes easily.
It is free.