Yes. Mueller's charge is to follow any path that leads to uncovering Trump's criminality.
Cohen, his lawyer/fixer, is likely facing disbarment for breaking campaign finance & disclosure laws.
Also, here's NYC's rule of professional conduct 1.8(e) (for attorneys - isn't he a member of the NY bar?):
(e) While representing a client in connection with contemplated or pending litigation, a lawyer shall not advance or guarantee financial assistance to the client, except that:
(1) a lawyer may advance court costs and expenses of litigation, the repayment of which may be contingent on the outcome of the matter;
(2) a lawyer representing an indigent or pro bono client may pay court costs and expenses of litigation on behalf of the client; and
(3) a lawyer, in an action in which an attorney’s fee is payable in whole or in part as a percentage of the recovery in the action, may pay on the lawyer’s own account court costs and expenses of litigation. In such case, the fee paid to the lawyer from the proceeds of the action may include an amount equal to such costs and expenses incurred.
PDF of the NY rules available at:
NYSBA | NYSBA | Professional Standards for Attorneys
Is paying someone to shut up a "court cost" or "expense of litigation"?
:thinking
I'm too lazy to dig further. It's a Sunday. I'm not even sure I have access to NY bar overseer disciplinary actions, but come to think of it, they are the sort of thing that is probably publicly available on the overseers' site
(oddly enough, the first result for "NYC bar overseers disciplinary decisions" is the Massachusetts disciplinary decisions).
Note: if he
is subject to an ethics investigation, than other portions of the rules (1.6(b)(5)(i) allow him to disclose confidential information to the extent he reasonably believes it necessary to defend himself from accusations of wrongful conduct.
As for election law, it's unrelated to Mueller's investigation, so Sessions isn't recused. What's the probability that Sessions is going to direct the DOJ to look into Cohen's payment on behalf of Trump? I don't think it's particularly likely that anything related to Daniels is going to hurt Trump in regard to Meuller. It's just some sordid little affair from years back, and the only person who seems to have potentially implicated himself is Trump's lawyer.
(On the other hand, if Daniels had the affair, then demanded money
or else she would go public, she may have walked herself into a blackmail/extortion problem. But it doesn't sound like that is the situation. It sounds like Trump offered the hush money of his own accord - or if we want to assume his innocence, Cohen did - and I don't think that's illegal. It's not like he'd be paying her to to commit a crime, etc.).