Is it possible to break supersymmetry in such way that the SUSY partners of the known particles have a much lower mass as opposed to greater? To continue, is it possible to break SUSY in a way that leaves some of the SUSY partners about equal in mass?
These issues arose in connection with an unpublished ab initio calculation of the cosmological constant correct to one order of magnitude (when parameterized by the WMAP data). The attempt to understand how the assumptions behind this calculation affects the dark matter/energy question lead to the submitted question.
 A: 
Is it possible to break supersymmetry in such way that the SUSY
  partners of the known particles have a much lower mass as opposed to
  greater?

This is very difficult to do because there are a variety of experimental bounds that disfavor these models. 
Particle colliders, culminating in the Large Hadron Collider, have excluded that parameter space for all relatively naive versions of Supersymmetry, whose superpartners must have very specific properties (i.e. spin, charge, weak force interactions), in order to be partners of the Standard Model particles. One representative exclusion chart is this one:

From a post at this blog of an LHC scientist posted in 2011.
As this chart shows, the LEP and Tevatron experiments (D0 and CDF) had already excluded the light SUSY partner parameter space before the LHC even opened for business.
If they existed, light sparticle pairs should appear in weak force boson (i.e. W and Z boson) decays, which they do not. And, the data increasingly disfavors the presence of Higgs boson portal decays in models that seek to avoid the constraints facing naive SUSY models in which the Higgs boson is the only Standard Model particle the sparticles interact with (see also here).
Light sparticles also ought to give rise to a discrepancy between the theoretical and experimentally measured value of the magnetic moment of the muon (muon g-2) that is much larger than what is observed (because masses close to that of the muon have more of an impact on muon g-2 than masses much greater than that of the muon where the heavy particles "decouple" from the lighter particles' behavior). 
The leading proposals for SUSY superpartners are in somewhere in the 5 TeV+ to 600 TeV (i.e. 0.6 EeV) range. As one 2012 paper summed up the situation:

In this paper, we explore the potential consequences for the MSSM and
  low-scale SUSY-breaking. As is well-known, a 125 GeV Higgs implies
  either extremely heavy stops (≳10  TeV), or near-maximal stop mixing.
  We review and quantify these statements, and investigate the
  implications for models of low-scale SUSY-breaking such as gauge
  mediation where the A-terms are small at the messenger scale. For such
  models, we find that either a gaugino must be superheavy or the NLSP
  is long-lived. Furthermore, stops will be tachyonic at high scales.
  These are very strong restrictions on the mediation of supersymmetry
  breaking in the MSSM, and suggest that if the Higgs truly is at 125
  GeV, viable models of gauge-mediated supersymmetry breaking are
  reduced to small corners of parameter space or must incorporate new
  Higgs-sector physics.

But, another such paper noted that the Higgs boson indirectly places an upper bound on supersymmetric particle masses, which would potentially rule out SUSY partners existence entirely:

The LHC is putting bounds on the Higgs boson mass. In this Letter we
  use those bounds to constrain the minimal supersymmetric standard
  model (MSSM) parameter space using the fact that, in supersymmetry,
  the Higgs mass is a function of the masses of sparticles, and
  therefore an upper bound on the Higgs mass translates into an upper
  bound for the masses for superpartners. We show that, although current
  bounds do not constrain the MSSM parameter space from above, once the
  Higgs mass bound improves big regions of this parameter space will be
  excluded, putting upper bounds on supersymmetry (SUSY) masses. On the
  other hand, for the case of split-SUSY we show that, for moderate or
  large tan⁡β, the present bounds on the Higgs mass imply that the
  common mass for scalars cannot be greater than 1011  GeV. We show how
  these bounds will evolve as LHC continues to improve the limits on the
  Higgs mass.

This isn't to say that theorists haven't tried to imagine SUSY theories with low mass superpartners, but there is zero affirmative experimental evidence to back up these proposals (the theories try to tailor themselves to portions of parameter space that are not definitively ruled out even though there are no positive signals of SUSY phenomena).

is it possible to break SUSY in a way that leaves some of the SUSY
  partners about equal in mass?

Since there are very few bounds on sparticle masses theoretically, this is certainly a possibility that has been considered and isn't ruled out any more than other SUSY theories. Some SUSY theory proposals conclude that sparticles are all similar in mass.
