The Privy Council recently summarised the common law in relation to cross-examination on credit, in Clarke v The State  UKPC 16 at :
At common law, therefore, the judge had a discretion to permit cross-examination as to credit. In exercising that discretion he was required to have regard to whether such questions would seriously affect the jury’s view of the credibility of the witness, to whether the misconduct relied upon had a solid foundation, to the fairness to the witness of permitting such cross-examination and to whether such cross-examination would be a distraction from the real issues in the case. An appellate court may not interfere with the exercise of such a discretion unless it is clearly wrong or wrong in principle.
Because it is a matter of discretion, it is not possible to say definitively whether the proposed questions are permissible “merely because Wayne is Dan's neighbour.” However, questions about whether the witness is biased against a party are generally allowed. In Attorney-General v Hitchcock (1847) 154 ER 38 at 42, Pollock CB said:
It is certainly allowable to ask a witness in what manner he stands affected towards the opposite party in the cause, and whether he does not stand in such a relation to that person as is likely to affect him, and prevent him from having an unprejudiced state of mind, and whether he has not used expression importing that he would be revenged on someone, or that he would give such evidence as might dispose of the cause in one way or the other.
As for the admissibility of convictions to impeach the credit of a witness: “there is not a little obscurity about the extent of the common-law principle concerning the use of convictions for this purpose. It must be remembered that until the Evidence Act 1843 conviction of felony or any crimen falsi rendered a man incompetent as a witness. This limited the possible occasions of the question arising”: Bugg v Day (1949) 79 CLR 442 at 465. Thus, the admissibility of such evidence depends on the statute law of the jurisdiction in question and cannot be determined solely by reference to the common law.
However, by the time of Wigmore’s Treatise on the Law of Evidence (16th ed, 1899), it was possible to say (at 578):
… proof by the record of conviction of crime is universally conceded to be a proper mode of impeachment. As to what kinds of crimes may here be employed, there is no general agreement. When conviction as a ground for total disqualification was abolished by statute, the statute usually provided for the use of such evidence in impeachment, and accordingly the statute often indicates the precise range allowable. Where it does not, the question may arise whether the kinds of crime are to be the same as were formerly sufficient to disqualify, or whether they are to be limited to those which affect the trait of veracity. In most jurisdictions the former solution is reached.
There is one other principle which should be noted, since the question suggests that cross-examining counsel might ask speculative questions “in the hope to uncover any reasons why Wayne would be biased against Dan.” There is a potential ethical problem here if the questions have no basis (ie. they are not even supported by Dan’s instructions). Lord Reid summarised the relevant principle in Rondel v Worsley  1 AC 191, at 227:
Every counsel has a duty to his client fearlessly to raise every issue, advance every argument, and ask every question, however distasteful, which he thinks will help his client's case. But, as an officer of the Court concerned in the administration of justice, he has an overriding duty to the Court, to the standards of his profession, and to the public, which may and often does lead to a conflict with his client's wishes or with what the client thinks are his personal interests. Counsel must not mislead the Court, he must not lend himself to casting aspersions on the other party or witnesses for which there is no sufficient basis in the information in his possession, he must not withhold authorities or documents which may tell against his clients but which the law or the standards of his profession require him to produce.