For historical reasons, during the Great Fast there are really two day-night cycles going on - one the usual order beginning at Vespers, and one running from midnight to midnight. Also, there are no hard and fast rules for the melodies used in the common parts of the services; a lot depends on local tradition.
Monday through Friday are fasting days; the Eucharist is not celebrated except on the feast of the Annunciation (when it is held in the evening on the feast itself).
In churches that use prostopinije, the "Lenten melody" for responses may reasonably be used at all services on Monday morning through Friday evening.
Saturday and Sunday are Eucharistic days, on which the Divine Liturgy of St. John Chrysostom (Saturdays) and St. Basil (Sundays) would normally be celebrated. Lenten melodies would NOT be used from Saturday morning through the late afternoon of Sunday.
Great Vespers and Sunday Matins are celebrated as usual on Saturday evening and Sunday morning, and the hymns of the Resurrection in the tone of the week are combined with the hymns of the Triodion. (I am not sure I understood your comment above, but the Liturgy of the Presanctified Gifts is never celebrated on Saturday evening.)
Vespers on Sunday evening is a special case, since this service returns us to the more strict fast of the weekdays. By tradition, the service begins with the usual melodies, and moves to the Lenten form of the service halfway through.
Please note that the Liturgy of the Presanctified Gifts largely fell out of use for several decades, and with it the so-called "Lenten melody." During its gradual re-introduction, some parishes chose to use the Lenten melody for other services on Lenten weekdays, and some used it as "the Presanctified melody." Again, there is no strict rule; it is a matter of custom.