The main effects on wound healing (which is what this is) and the immune system with age are for them to decline. The wound healing is partly due to the effects of glycation (addition of sugar molecules to proteins over time) on proteins involved in healing (such as growth factors) and in the structure of the tissue (collagen mainly). This happens slowly over time. If you have impaired healing due to this then the bruises should last longer because it takes longer for the damaged vessels to be repaired.

As for the menopause this can affect many things but I don't think any of them are beneficial. The decline of the immune system with age is more closely linked to the adrenopause, which is decline in the function of the adrenal gland, and the increase in the ratio of cortisol/DHEA that this causes. Relatively more cortisol means a poorer immune system.

Both systems can be influenced by anti-oxidants (there is evidence that vitamin E is beneficial as an anti-oxidant in wound healing) so a healthy, balanced diet full of vitamins and the like will help keep both systems running. The last time I checked (about 5 years ago) there is a possibility that supplementation with DHEA may be beneficial in offsetting the effects of age (I did some of this research myself) but there had not been a comprehensive clinical trial.