The usual pattern for the verb unterstellen is this:
Jemand unterstellt jemandem etwas.
Someone insinuates something to someone else.
Der Staatsanwalt unterstellt dem Angeklagten einen Mord.
The prosecutor insinuates a murder to the defendant.
(The prosecutor alleges that the defendant committed murder.)
An alternative pattern is this:
Jemand unterstellt jemandem, <Nebensatz>.
Someone insinuates to someone <subordiante clause>.
Der Staatsanwalt unterstellt dem Angeklagten, einen Mord begangen zu haben.
The prosecutor insinuates to the defendant to have committed a murder.
(The prosecutor alleges that the defendant committed murder.)
Daglo unterstellt al-Burhan, sein Amt als De-Facto-Staatschef nicht aufgeben zu wollen.
Daglo insinuates to al-Burhan that he does not want to give up his post as de facto head of state.
(Daglo insinuates that al-Burhan does not want to give up his post as de facto head of state.)
- jemand
In English: someone
In the example sentence: Daglo (name of a person in nominative case)
Subject and therefore in nominative case.
It names the person who makes an assertion.
- unterstellt (a grammatical form of unterstellen)
In English: to presume, to assume, to imply, to insinuate
The verb of the sentence
It names the kind of action.
- jemandem (a grammatical form of jemand)
In English: to someone else
Object in dative case.
In the example sentence: al-Burhan (name of a person in dative case which in this example looks identical to nominative case)
It names the person who is claimed to be responsible for something.
- etwas
In English: something
An object in accusative case.
It names the thing that the person in dative case is claimed to be responsible for.
- <Nebensatz>
A subordinate clause.
In the example sentence: sein Amt als De-Facto-Staatschef nicht aufgeben zu wollen (The assumption that Daglo makes about al-Burhan.)
It describes the thing that the person in dative case is claimed to be responsible for.
Yes you are right, in the other sentence is an error. This would be correct:
Unklar war zunächst, wer die Schüsse abgegeben hat.