The first observation of a 3.5keV line, i.e. as a decay product of a 7keV neutrino is probably "Detection of An Unidentified Emission Line in the Stacked X-ray spectrum of Galaxy Clusters"; Esra Bulbul, Maxim Markevitch, Adam Foster, Randall K. Smith, Michael Loewenstein, Scott W. Randall (2014)
who's abstract says (emphasis added):
We detect a weak unidentified emission line at E=(3.55-3.57)+/-0.03 keV in a stacked XMM spectrum of 73 galaxy clusters spanning a redshift range 0.01-0.35. MOS and PN observations independently show the presence of the line at consistent energies. When the full sample is divided into three subsamples (Perseus, Centaurus+Ophiuchus+Coma, and all others), the line is significantly detected in all three independent MOS spectra and the PN "all others" spectrum. It is also detected in the Chandra spectra of Perseus with the flux consistent with XMM (though it is not seen in Virgo). However, it is very weak and located within 50-110eV of several known faint lines, and so is subject to significant modeling uncertainties. On the origin of this line, we argue that there should be no atomic transitions in thermal plasma at this energy. An intriguing possibility is the decay of sterile neutrino, a long-sought dark matter particle candidate. Assuming that all dark matter is in sterile neutrinos with m_s=2E=7.1 keV, our detection in the full sample corresponds to a neutrino decay mixing angle sin^2(2theta)=7e-11, below the previous upper limits. However, based on the cluster masses and distances, the line in Perseus is much brighter than expected in this model. This appears to be because of an anomalously bright line at E=3.62 keV in Perseus, possibly an Ar XVII dielectronic recombination line, although its flux would be 30 times the expected value and physically difficult to understand. In principle, such an anomaly might explain our line detection in other subsamples as well, though it would stretch the line energy uncertainties. Another alternative is the above anomaly in the Ar line combined with the nearby 3.51 keV K line also exceeding expectation by factor 10-20. Confirmation with Chandra and Suzaku, and eventually Astro-H, are required to determine the nature of this new line.(ABRIDGED)
The general theory of the decay of sterile neutrino dark matter goes back a ways. "Sterile neutrino hot, warm, and cold dark matter; Kevork Abazajian, George M. Fuller, and Mitesh Patel
Phys. Rev. D 64, 023501 – Published 31 May 2001" is a common reference, but it's a general paper that follows on specific work, mostly from considerations of the early universe. Pages 13 and 14 briefly discuss sterile neutrino decay, without specific mention of a particular mass or decay line.
Earlier there's "New cosmological limit on neutrino mass; Fuller GM, Malaney RA. Phys Rev D Part Fields. 1991 May 15;43(10):3136-3139." but note that even then it's considered a new cosmological limit; general discussions in terms of cosmological limits were happening in the 80's or before.
The 2006 "Direct X-ray Constraints on Sterile Neutrino Warm Dark Matter" paper referenced in the question should not be considered as raising a 3.5keV line hence a 7keV neutrino. It explicitly works from the opposite case:
Several direct limits on ms have already been reported. The absence of anomalous line features in XMM-Newton (0.5−12 keV) [55, 56] and HEAO-I (3−60 keV) [57, 58] measurements of the Cosmic X-ray Background (CXB) allowed Boyarsky et al.  to set a (95% C.L.) upper limit of ms < 9.3 keV (assuming, as with all the mass limits quoted below, that ΩDM = Ωs = 0.24). In Ref. , Abazajian, Fuller, and Tucker (hereafter AFT) suggested that the best constraints could be achieved by examining individual objects, e.g., galaxies and/or clusters, rather than the CXB. Based on XMM-Newton observations of Virgo A (M87), the dominant galaxy in the northern part of the Virgo cluster , Abazajian  arrived at an improved upper limit of ms < 8.2 keV (95% C.L.). Boyarsky et al.  have also used XMM-Newton observations of Virgo A  and the Coma [62, 63] cluster to explore possible constraints on ms, but they do not provide a definite numerical limit. Abazajian and Koushiappas  estimate an upper bound of ms < 6.3 keV (95% C.L.) based on the results in Ref. .
(ms there is the mass of the sterile neutrino)
Their technique was not based on any specific decay line, but rather based on the absence of them in a diffuse background:
We use the diffuse X-ray spectrum (total minus resolved point source emission) of the Andromeda galaxy to constrain the rate of sterile neutrino radiative decay.
They did this by setting limits on a range of possible masses, as shown by example in their Figure 1:
They only considered a 7keV mass as one of a range. Further, their abstract shows that they ruled out (at 95% CL) the existence of the 7keV neutrino hypothesis now being studied, at least in the observations they considered:
Our findings demand that ms < 3.5 keV (95% C.L.) which is a significant improvement over the previous (95% C.L.) limits inferred from the X-ray emission of nearby clusters, ms < 8.2 keV (Virgo A) and ms < 6.3 keV (Virgo A + Coma)
Starting from all the above, we can answer the specific questions given:
What is the first paper to have hypothesized a sterile neutrino, the decay of which would produce a line at about 3.5keV?
The 2014 Bulbul et al observation of the 3.5keV line led to the specific proposal of a 7keV neutrino. Before that, there appear to be proposals for neutrinos without a specific mass.
Was the mass a consequence of a theory without adjustable parameters for the sterile neutrino or was it an attempt to explain observation as in the aforelinked paper on X-Rays?
It was part of an observational paper, though the 2014 one, not the one linked in the question. There were certainly general theories, a whole range of those existed; they just didn't make specific predictions.
If it was a theory with adjustable parameters for the sterile neutrino mass, what was the range of masses permitted by the earliest such theory and what was the range of their decay emission photon energies?
Depends a lot on how hard you want to look, but the predictions certainly cover orders of magnitude. If you accept such a wide range as being "seminal", then Abazajian, Fuller, and Patel (2001) is probably the best bet for the seminal paper.
In the comments on this answer, there was also a request for
identification of the earliest paper to have hypothesized a sterile neutrino mass -- even if it had adjustable parameters permitting a range of mass to be constrained by observation -- the decay of which would predict that we should expect to see emission lines in the approximate range of 3.5keV.
That's not really how this part of dark-matter physics works. There are many hypotheses for possible particle species, interactions and decays; whole conferences of them. The experimentalists have to look where they can, slowly expanding that area as technique and opportunity allow. When there was a chance to look at keV-range X-rays, they did. They they looked harder. And again, even harder. There was nothing like "we should expect to see emission lines in the approximate range of 3.5keV", just that we could.
As evidence for this, consider the Dark Matter 2014 conference, the closest big one to the observation paper, which has almost no discussion of keV-scale neutrino theory. It was all about Fermi, 10's of GeV gammas and the Hooperon. Low mass was the realm of "heavy axions". The only discussion of neutrinos was in a single, almost-prescient talk by George Fuller (UC San Diego, same as GM Fuller on the 1991 paper) which covered the theory and pointed back to Abazajian, Fuller, Tucker (2001), updated with recent non-astro-experimental work:
then went on to talk about "Possible Detections" including Bulbul et al.
The situation at the Dark Matter 2012 situation was even bleaker from a sterile neutrino prediction point of view. Both George Fuller and Alexander Kusenko spoke, but there wasn't anything specific in either set of slides. George's had over 3 orders of magnitude on the mass axis.
So there was certainly theory work on what sterile neutrinos might look like in a large mass range, which was quickly used to understand the observation(s) as they appeared, but there was no reason to believe this was "more predictive" than work around 0.001 eV or 100 GeV possibilities.