What rights are corporations actually given?
Rights Corporations Have
Primarily economic rights such as the right to own and transfer property, the right to enter into and enforce contracts, the right to sue for harms to property interests and breaches of contracts, the right to eminent domain compensation for takings of property, the right to employ agents and hire employees, and the right to intellectual property rights in trade names and trademarks.
But, also, the right to engage in commercial speech, to petition the government, the right to a jury trial, and the right to due process. Corporations can enjoy attorney-client and accountant-client privileges for their confidential communications, but not doctor-patient, spousal, clergy-parishioner, or therapist-client privileges.
Rights Corporations Lack
On the other hand, corporations do not have the right not to self-incriminate themselves, outside some very narrow circumstances they cannot vote, and they do not themselves have the freedom of religion in most cases (although there are exceptions for religious institutions and when the religious rights of owners of closely held entities are affected).
Corporations do not necessarily have the right to bear arms. Corporations do not have rights inherent in human form (e.g. the right to obtain an abortion or use contraception, the right to be free from excessive corporal punishment, the right to raise children without undue interference, the right to not be owned or enslaved).
Corporations do not have the right to have debts discharged in a Chapter 7 bankruptcy. Corporations are not entitled to exempt any other their assets from creditor's claims. Corporations do not have the right to represent themselves in court without a lawyer or to serve on juries. Corporations do not have the right to apply for most kinds of government jobs or to run for office. Corporations are not eligible for most ordinary welfare programs (like TANF, food stamps, Medicaid, Social Security, disability payments, veteran's benefits), but are eligible for a variety of tax credits and business grants, which are often called "corporate welfare" (even though almost all "corporate welfare" is also available to sole proprietors and general partnerships).
While corporations cannot be "drafted" into a war like humans, they can be compelled to carry out governmental tasks in wartime.
What was the purpose and law that created this concept?
One reason was to allow passive investors to pool investments for a business purpose in exchange for a share of profits and a return of investment, much like a lender would, without liability in excess of the amount invested, thus limiting the risk of investing in a venture that could be a horrible failure.
Closely related was the goal of separating management and ownership, so that the economic value of an operating business could be transferred from one passive owner to another without interfering with or impacting the operation of the business. Corporations made it easier to be a true "capitalist", i.e. someone who generates income from ownership of property with economic value that is made available to businesses, without actually being a skilled manager or producer within a business. Before corporations and business trusts, all business owners had the right and obligation to manage the business and unlimited liability for any debts incurred by the businesses in which they invested even if they had no personal fault in causing that liability other than making their funds available for someone else to use in exchange for a share of the profits from the business.
Another purpose was to protect the public and customers from the operations of complex enterprises and businesses by allowing them to hold the enterprise liable without knowing who in particular in the enterprise harmed them in precisely which manner. As long as it can be shown that somehow the enterprise or someone in it caused harm, it can be held accountable and none of its assets can be shielded out of a desire to protect the personal survival and well being of a natural person (who would normally have exemptions from creditors).
Similarly, vendors and creditors and customers can hold the corporation responsible even if the management and employees all change over time, its headquarters relocated, etc., without having to deal with renegotiating any contracts regarding sources of payment or who in particular must fulfill the corporation's obligations.
In English law, the earlier development was the trust, in which a human being was given assets to manage subject to certain terms rather than as his own property, for the benefit of other beneficiaries, without having personal liability for the trust assets except due to his own personal management of those assets.
An important transitional form was the "corporation sole" (which is how the Roman Catholic church is organized) in which a single person, usually a high ranking clergyman acted as what we would now call a trustee with respect to all of a non-profit institution's property and rights, and could pass all of that property and all of those rights as a single unit to a successor to the same position, but unlike an aristocrat, the embodiment of a corporation sole was not entitled to use the assets of the corporation for personal benefit beyond what was necessary for his humble personal needs pursuant to vows of personal poverty.
The earliest private, investor owned corporations, like the East India Company, were created ad hoc by individual pieces of legislation, much like we might create a stadium authority or transportation district today. Towards the end of the 19th century and beyond, general statutes allowing particular kinds of corporations (e.g. ditch companies, or railroad companies) were established, and later, general corporate statutes were adopted.
These statutes were also informed by the case law of fiduciary duties created for trusts, estates, partnerships, and in agency law, by common law tort doctrines such as vicarious liability (originally developed for natural persons with employees and agents), by a common law of commercial property and contracts related to such property, by tax laws, and so on. Accounting customs and practices also became enmeshed in corporate law.
In the 20th century, especially in response to the Great Depression, a new class of regulatory laws called "securities laws" regulated big businesses with many shareholders and the marketing of shares in these kinds of companies to members of the general public.
Is it possible for a 'natural' person to get the benefits of an
There are really no rights that an artificial person has that a natural person does not.
The notion that corporations have rights that adult human beings do not is mostly a myth that is really targeted at the abuses of big businesses generally, something that was an issue in the days of large sole proprietorships and partnerships and trusts long before the corporate form was widespread.
Corporations can insulate business owners (especially passive investors) and business managers from civil liability for broken contracts and from torts difficult to localize to a single person, in ways that would be difficult to achieve for sole proprietors or partners in a general partnership. But, the corporations themselves don't have rights or privileges beyond those of human beings.
Also, a "natural person" can create a solely owned corporation or limited liability company (or many of them) for a trivially small filing fee (often $50) and very modest legal fees from a private lawyer if the natural person doesn't do the work without the assistance of a lawyer, if they find it useful to do so.