Suggested answer:
(1) All three quantifiers occur with both singular and plural concord in the corpus. Singular and plural concord with a series of:
A series of his speeches survives celebrating individual gods...
A series of dormer windows were cut into the roofs...
Singular and plural concord with a group of:
A group of Sikhs has spread a cloth on the ground and is eating...
A group of sullen men were ranged along the bar...
Singular and plural concord with a collection of:
... and a collection of his compositions was recently published to commemorate...
A collection of Broadway shopping bags sit on the table.
(2) The choice of concord seems to be linked to the way the head noun is viewed, either as a fixed set (singular concord) or as individual members of that set (plural concord). If we stress the fact that it was a group of Sikhs, rather than several individual Sikhs, we use a singular verb form. However, if we wish to stress that the group consisted of several individual members, we use a plural verb form.
(3) No, the three head words seem to prefer singular concord when they are used in combination with the definite article, although in the case of the collection the corpus returned very few occurrences where it was found in combination with a verb showing concord.
Examples from the corpus of the series, the group, and the collection with singular concord:
Since 1980 the series has been sponsored by PPG Industries...
The group keeps moving about...
Penelope realized the collection was not all to J.D.'s taste...
Although the tendency is for all three to prefer singular concord, there are instances where the group takes plural concord, e.g.
I joined the group who were making their way back to the pavilion.
Read about concord here and here, and about Subject-Verb agreement and expressions of quantity here
Terminology: concord, singular, plural, quantifier