Can Journals settle all legal processes related to accepted papers before publication on behalf of authors? For an accepted paper about to be produced (not open access), the author should agree to terms that all illustrations, tables etc. have recieved permissions from the copyright owner. If the author agrees, the paper takes the copyright of the Journal. The question is that, for an inexperienced author, could the journal take up the responsibility (e.g through an office) to take care of issues of permissions etc. before beginning the production process? Thus, they would look into: which figures, tables etc. require permission and they would go through the process. For instance using a Rightslink account etc.

Edit: If not, could they (at least some of them) offer advice on what and what may require permissions from an accepted manuscript?
This isn't usually done. The authors are assumed to have gotten the permissions themselves. However your question is whether the journal "can". In that case, I'd say the answer is yes. They can, they just don't usually do it. Just about the only possible exception is if the author is a famous researcher and the journal is willing to go to great lengths to publish the manuscript.