Is it permissible to audibly and collectively engage in dhikr and praise between the Adhan and the Iqamah?

If the congregation performs these invocations collectively at a specific time, this falls under the category of an additive innovation (bid'ah idafiyyah), and it causes disturbance to those in the mosque. They should be advised gently and wisely to cease what they are doing. As for praises specific to the Prophet, peace be upon him, there is detail regarding them. The general principle is that performing the remembrance of Allah silently is better to preserve sincerity, unless there is a benefit resulting from performing it aloud.