Does the European Council have the power to dismiss the European Commission at any time?
No; the Commission is responsible to the Parliament, not to the Council, as stated in article 17 subsection 8 of the Treaty on European Union:
The Commission, as a body, shall be responsible to the European Parliament. In accordance with Article 234 of the Treaty on the Functioning of the European Union, the European Parliament may vote on a motion of censure of the Commission. If such a motion is carried, the members of the Commission shall resign as a body and the High Representative of the Union for Foreign Affairs and Security Policy shall resign from the duties that he carries out in the Commission.
Only the High Representative of the Union for Foreign Affairs and Security Policy – who, by virtue of their office, acts as a member of the European Commission, too – can be removed from office by the European Council. It’s also the European Council that appoints the High Representative.