To assess protein stability you could try molecular dynamics based approach (doi:10.1016/j.bpj.2010.01.051) or Rosetta based calculation (DOI:10.1002/prot.22921).
To predict pKa shifts an alchemical MD approach could be taken similarly to that of protein thermostability calculations. Another way is to use an empirical predictor, e.g. Propka (DOI: 10.1021/ct100578z)
For aggregation prediction could try Tango (doi:10.1038/nbt1012) or Zyggregator (doi:10.1016/j.jmb.2008.05.013).