Validity of Henry's Law for an Oxygen/Bitumen System?
Regarding Q1, Henry's law states:


  At a constant temperature, the amount of a given gas that dissolves in
  a given type and volume of liquid is directly proportional to the
  partial pressure of that gas in equilibrium with that liquid.



A1 is answered by the definition itself: the system should be at equilibrium.  
A2 is straightforward: if the gas reacted, you would not have a constant pressure as a certain (if not all) quantity of it would be removed from the system[1]. This would also keep your system from being at equilibrium, defying the previous assumption.
A3 and A4 both depend on the fact that – as the concentration or the partial pressure rise – the system deviates from an ideal model where the solute is
infinite-diluted and in such system Raoult's Law should be used
instead[2]. So you need a low concentration and partial pressure of your gas.  


To answer to Q2, Henry's Law can be applied to any solvent, whether liquid, vapour or solid[3], [4]. It has been used, within certain limits, to study absorption of gas in zeolites[5] or hydrogels, but I couldn't find any precise experimental data on it. Only that in such systems it is only a limited law, adequate at low mole fractions, but useful for practical purposes when high precision is not required.

&nbsp;&nbsp;&nbsp;&nbsp;1 Henry's Law, UC Davis University ChemWiki
&nbsp;&nbsp;&nbsp;&nbsp;2 North Carolina State University, CH 431 / Lecture 14
&nbsp;&nbsp;&nbsp;&nbsp;3 Francis L. Smith and Allan H. Harvey (September 2007). "Avoid Common Pitfalls When Using Henry's Law".
&nbsp;&nbsp;&nbsp;&nbsp;4 Rosenberg, Robert M., Peticolas, Warner L., Journal of Chemical Education, Volume 81, 11, pp 1647-1652
&nbsp;&nbsp;&nbsp;&nbsp;5 Eric G. Derouane, Zeolites as solid solvents, Journal of Molecular Catalysis A: Chemical, Volume 134, 1–3, pp 29-45