I see that Senate Republicans are making dissatisfied noises about some of Biden's cabinet choices.
Yeah, the joke is that he hasn't yet chosen a single member of his family. What's up with that?
What power do they have regarding the confirmation hearings for those cabinet members?
Quite a lot, if the Republican Party maintains its majority. This is why the outstanding Senate races are so important.
For example, if they vote against a nomination does that mean Biden has to choose someone else?
Yes.
Or, more disruptively, can they just decide not to bother with hearings, as they did with Obama's judicial nominations?
Yes.
However, to remedy both these cases the positions can be filled with acting secretaries, administrators, and so forth. In fact, this is what Pres. Trump has preferred to do in some cases. If an appointee is voted down, he can no longer serve in the acting role. If he's never submitted for confirmation, he's safe in his acting role. While the confirmation vote determines whether the appointee will take office, the minority party in Senate confirmation hearings has the right to invoke Congressional investigative powers to discover things about the candidate and ask him or her questions that the President may not want heard in public. Even if the appointee is eventually confirmed, pointed questions from the minority committee members can do political damage. So if you want to appoint an unscrupulous person to a Cabinet position, you accept the limitations of the acting Secretary role and never submit the name for confirmation.
At the Cabinet level, acting Secretaries don't have discretionary authority. In many cases they can only be caretakers of existing policies, rules, and functions. If you want a successful administration, it pays to have a strong Cabinet position, which can only come from Senate confirmation. But the answer to your partially-stated question is yes, Sen. McConnell and a hostile Senate can do much to hobble the Biden Administration by denying him the service of an effective Cabinet.