Can a divorced person without a Church annullment participate in the sacrament of confession or can that person not participate in any sacrament (e.g., last rites, before death etc.)?
A divorced person is generally not required to seek an annulment unless he or she plans to attempt marriage again. And unless a person has been excommunicated (divorce is not cause for excommunication) a Catholic always has access to confession. In fact, a divorced Catholic should go to confession as soon as possible if the divorce was the occasion of mortal sin.
What other sacraments are available? Assuming one is already baptized and confirmed these sacraments cannot be repeated. A civilly divorced person is really still married so matrimony and holy orders are not available. That leaves only the Eucharist and Anointing of the Sick both of which are available provided one is properly disposed.