1. In cases of motions to reconsider nominations:
Senate Rule XXXI (4) states that the Secretary of the Senate shall not transfer confirmation or rejection of a nomination to the President until the expiry of the period to bring a motion to reconsider (on the same day on
which the vote was taken, or on either of the next two days of actual
executive session of the Senate), or while a motion to reconsider is still pending, except with unanimous consent of the Senate.
If this has taken place, and a motion to reconsider is brought after the nomination has been transferred to the President, "the motion to reconsider shall be accompanied by a motion to request the President to return such notification to the Senate".
Riddick's Senate Procedure further provides the following predecent:
Where a nomination has been sent to the President, a motion to
reconsider must be accompanied by a motion to request the President to
return the resolution of notification, but the President may refuse
the request. The Senate has no power to reconsider any nomination, if
the President, upon request of the Senate, refuses to return the
resolution of notification.
As precedent, it cites the case of the April 25th nomination of John W. Kern to the US Tax Court in 1950, when the Senate requested the President return his confirmation resolution on May 9th. The President refused, as the Senate had overruled Senate Rule XXXI (4) by unanimous consent, he had already signed Kern's commission on April 25th, and Kern had entered into the role. A similar case occurred in 1939 with the nomination of Elmer D. Davies to be a district judge.
Furthermore, in 1932, in United States vs. Smith, the Supreme Court held that if the President refuses to return a nomination resolution, the Senate has no power to reconsider said nomination.
2. After a bill has been sent to the President, but not signed:
This is covered in the answers to this question - the answer appears to be that the Senate cannot reconsider once a bill has been transmitted to the President for their signature.
3. After a bill has already been signed by the President into law:
No, once an act has been signed into law, the Senate cannot bring a motion to reconsider its vote. A new act would have to be passed nullifying the original act.
The motion to reconsider remains effective on positive votes in theory, because the idea is that Secretary of the Senate does not act on the vote until there is no possibility of a motion to reconsider. In practice, the Senate usually overrules this via unanimous consent, but it is perfectly capable of not doing so.