This is a really interesting question and one that can be approached in many ways depending on region, state, or years of interest. For the sake of time, I'll answer this from a more general perspective, and use specifics when I can. I'll use the perspective of those who were enslaved primarily in the Revolutionary Era, but will also try and address the 19th century even though that isn't my specialty. So I'm going to answer your second question first, since mortality rates are important to understand prior to knowing how their lives fared after they reached old age.
Generally speaking, many slaves did not live to "old age" as one may put it. For starters, many historians have poured themselves into the research into most enslaved people's first experience with slavery: the middle passage. Historians have suggested that at least around 4.5% of slaves died while on shore prior to their deportation and 12.5% of slaves died during the passage over to the New World, and another 7.5% died during "seasoning" once they reached their destination.. From here, mortality rates were entirely dependent upon where an enslaved person ended up. Enslavement in the Caribbean, for instance, was much harsher than being more north in the American Colonies. Conditions were so terrible, that slave owners like George Washington used the threat of selling their slaves to owners in the Caribbean against their own slaves because their slaves had heard the horrors of the West Indies. (Washington even did this on several occasions to different slaves.) Also worth noting that only about 6% of all enslaved Africans were sent to the American Colonies, with the majority of the rest heading to the Caribbean and South American colonies.
Life in the American Colonies were difficult for enslaved persons even if they had "good" masters. Slaves typically worked from dawn until dusk if they worked outside, and even slaves who worked inside had long days although some slaves were given Sundays off (many kitchen or personal servants typically worked from 4AM to 8PM).
Babies had it even worse. It is estimated that about half of all enslaved babies did not survive until their first birthday. That same research institute also listed these as the biggest ailments facing slaves:
Common symptoms among enslaved populations included: blindness; abdominal swelling; bowed legs; skin lesions; and convulsions. Common conditions among enslaved populations included: beriberi (caused by a deficiency of thiamine); pellagra (caused by a niacin deficiency); tetany (caused by deficiencies of calcium, magnesium, and Vitamin D); rickets (also caused by a deficiency of Vitamin D); and kwashiorkor (caused by severe protein deficiency).
So what was the life expectancy of slaves? Not very high as most can imagine: [21.4 years old, verses over 25 years old for whites by 1850, with only 3.5% of the population living to be 60 years old(4.4% of white Americans lived to be 60 years old).] http://geriatrics.stanford.edu/ethnomed/african_american/fund/health_history/longevity.html). But, to be fair, reaching the age of 50 was considered old during this period.
So what happened to slaves when they got old? Well, a few things. First, if a slave happened to reach the age of 25, that individual was considered very valuable in most cases, causing slave owners to begin caring more for that individual's care. Second, some slave owners did free their slaves, and in some cases, like with George Washington, could free their slaves upon their death and with his personal servant, he even ensured he would receive a pension. Washington also decried that all slaves that were too old to work or move on to new professions were to be cared for at the estate while still gaining their own freedom. While Washington was able to free over 100 slaves this way, he was the only founder who owned slaves that did this.
Another factor is that impacted elderly slaves in many states were manumission laws. While these laws sometimes barred all slaves from being freed at various points in history, one important factor is that some manumission laws prohibited the freeing of slaves passed a certain age. For instance, in Maryland, that age was 45. This was done because many slave owners had a habit of using slaves for most of their youth, and then freeing them in their 50s, when they would be too feeble to work. These types of manumission laws were men to protect enslaved Americans by forcing slave owners to either free their slaves earlier, or be willing to take care of their slaves in their old age.
Taking care of old slaves was something that many slave owners opted to do in many cases, although using the terms "care for" is a loose term. In the best cases, slaves would be assigned simple tasks to complete in their old age, and in the rarest cases, slave owners would allow their slaves to retire on the property but their needs would still be taken care of by their masters. I cannot stress how rare this is ever recorded. (Old Age and the Search for Security: An American Social History pp. 93). This same book I just cited also outlines how slaves were still sometimes sold, even into their 60s if other owners still had needs for less physically demanding work. But again, this was rare to ever happen since only 3.5% of all African-Americans, including free African-Americans, lived until the age of 60.
Hope this answered your question. Let me know if you have any follow-ups.
Edit: grammar