Is it permissible to collect donations for the mosque between the Friday sermon and the establishment of the prayer, with the Imam waiting until the collection is complete, and does this not diminish the reward of the Friday prayer?

The default is to connect the sermon directly to the prayer. Some scholars are of the view that continuity (muwalat) is a condition for the validity of Jumu'ah (Friday prayer), otherwise the sermon becomes invalid due to a long interval. If the interval is related to the prayer, it does not matter. However, if the interval is long and unrelated to the prayer, such as collecting donations, the sermon becomes invalid. If it is short, it is excused. This is the view held by the majority of scholars. It is preferable not to separate the sermon from the prayer by collecting donations, in accordance with the guidance of the Prophet, peace and blessings be upon him, and so that the prayer does not become invalid due to a long interval. Donations can be collected after the prayer by placing boxes at the doors.