Unless I overlooked, it is strange Vitamin D is not mentioned here. It might not solve all the issues mentioned by the OP but is one of the best documented supplements to support the immune system. Many of us might be deficient or not sufficient in blood levels in particular as we age. Vitamin D receptors (VDR) are expressed on many tissues and are crucial for the macrophage functioning.
I would immediately test our 25OH Vitamin D level and supplement till I have a sufficient blood level. There are many discussion on this on LC and optimal doses and the following references might provide a starting points:
Prietl B, Treiber G, Pieber TR, Amrein K. Vitamin D and immune function. Nutrients. 2013;5(7):2502-21.
Sakem B, Nock C, Stanga Z, et al. Serum concentrations of 25-hydroxyvitamin D and immunoglobulins in an older Swiss cohort: results of the Senior Labor Study. BMC Med. 2013;11:176.
Holick MF. The D-lemma: to screen or not to screen for 25-hydroxyvitamin D concentrations. Clin Chem. 2010;56(5):729-31.