There is some free good help for you, but as with most things, you usually get what you pay for.
Your best bet for a free power of attorney for health care is the local hospital, preferably the one in which your mother might be hospitalized if needed. The patient representative there should provide you with one – and may even help by answering questions you may have about it.
Powers of attorney for finances are a bit trickier, and I know of no dependable free forms for them. You can get some good inexpensive help from some of the software programs available. And in the interest of full disclosure, I must divulge that I am one of the authors of such a product. I do not divulge this to push it, however -- only to let you to warn you from the inside out that there are a couple things to bear in mind so that you can shop around in an informed way.
When casting about for a product you can trust to produce a valid product, be sure that it produces documents that are keyed in to the particulars of your state law -- not just a template that claims to fit all with one size.
Also, check with the publisher to be sure that the product is updated frequently -- at least annually -- as the laws that control these documents change fairly frequently.
Your mother should also have a will or living trust that will allow her to direct who gets her property at her death. Again, you may be able to get inexpensive help with this from a self-help product, but mind the cautions noted above.
Other possible sources for free or inexpensive help: the self-help component of your local probate court if there is one, a local senior center, a legal clinic through a local law school. Finally, your Area Agency on Aging may be able to connect you with low-cost legal help for estate planning.