In the United States, who (individual, group of individuals, political party) has access to state voter lists that indicate whether or not the given registered voters had voted in (i) the last general election (ii) in any specific general election since each given individual was registered?
The question has not only who has the right, but also what is the liability to have the data.
Each state in USA and DC have their own laws and restrictions how voter data access is obtain and retain. Please take a look the updated Terms and Conditions link provided by Walklsits - a product of ScaleCampaign.
The actual right for access is determine by either public access to everyone(free and open to the world), Freedom of information Act (FOIA) request, or severe restrictions (see Terms and conditions link above).
For example for free access take a look state of Ohio:
The process of obtaining FOIA for some states goes into few steps: From SOS of each states, find the application under FOIA and submit request to obtain the data in question. Each state may restrict who as an individual has the right to submit FOIA for that state. That is done on state by state based. Below is an example of state of Michigan FOIA request that shows the answer and the actual data that was given in jump drive. Some states may issue CD via mail.
As a general rule, please read the state law and be careful how you store, distribute/share voter data.
For the items you mention, (i) and (ii) I can tell you that I, a member of the general public, have access to this information on my home computer.
It is my understanding that databases like this are sold to interested organizations.
Whether this is true in all the thousands of US voting jurisdictions, I can not answer