Can a member of the public gain access to information about any legal case?

Not in the UK. If a case has been widely reported in the press or if it has been the subject of an official law report, then such published information is available to the public. It is also possible for people with an interest in requesting this to obtain a court transcript (a very expensive business). However, most information on the court records is not for public inspection.Can a member of the public gain access to information about any legal case?
Pretty much. There are some cases that are ';sealed'; due to privacy interests (like child welfare or custody), or national security (like some ongoing criminal cases) or due to trade secret or confidential business communications (like when the KFC secret formula is litigated), but pretty much you can get anything that's been filed as a matter of public record, if you pay a copying (and sometimes per hour research) fee. You may have to know the county / state or district that the case has been brought in, the parties, and sometimes the case number for an accurate lookup, though.Can a member of the public gain access to information about any legal case?
Unless the case has been sealed, yes.
Yes and No. Most information about legal cases is public record. There are some documents which are not or are sealed. Those which are public record can be obtained by anyone. Many clerks have information online these days and that makes it easy to obtain.