Charity done during an eclipse is not tainted; so one can give or receive charity during that period.
Yes, it is considered special to do thirumanjanam and Tiruvaradhanam during the eclipse; but temples have to follow many ritualistic ordains as per the tradition, temples had to adhere strictly to the agamas like pancha rathra and hence their rituals vary as per their tradition. They must follow purifying rituals that are relevant to Perumal. There are many codes, traditions, rituals based on the scriptures. These are the ordains of the scriptures.
Punya kalam does not mean auspicious time per se; as performing bath, tharpanam during that period are considered special, it is called as punya kalam. There is something called eclipse-based taint and that taint is present always. It is also considered punya kalam, for example when we offer charity during that period, it is considered superior to that gifting during other periods. Hence performing charity, bath, tharpanam, japa, Tiruvaradhanam during this period is considered superior as it results in good benefits, states the scriptures. From another perspective, an eclipse is associated with certain dosham. So, the eclipse contains both punya kalam and dosham without any contradiction.
After performing vimocana snanam, one can proceed with daily austerities.