Here are my answers after the questions.
1. Does Hinduism have Temples or places of worship beside the shrines?
A: Shrines are in the memory of great saints and spiritual masters. Usually they are at a sacred place where a temple could be around. We in Bharat have many temples for a lot of devas and devis and god in different forms and names as given in the Vedic scriptures. The non-Vedics think we worship stones there. Mostly, they never inquired what we are worshipping, and how it works. Or, they do not have enough intelligence to understand it. Or, they hate it simply because it is not allowed in their Books.
2. If you do have Temples, is it for individual worship or do you have corporate times of worship when believers congregate or come together?
A: The whole world is a temple for the Vedic people. However, temples have been built at nice naturally beautiful and clean places like river bank, ocean shore, mountain top, etc. No temple is made by ordinary common people. They are built by the leadership and inspiration of some great saints or gurus. Common people then help as they could to build it. The soul of the temple is this saint/guru and his disciples after he/she departs. A temple is a dharma infrastructure for the society. It helps all to advance spiritually. Almost every one in Bharat will tell that just going to a temple and just sit there gives them peace. It is my experience as well.
Just putting a moorti (the idols as the non-vedics call it) does not make the place a temple. The Vedas provide a process of invoking life-force of the deity in the moorti. After that ceremony, called praaNa prathishThaa, the moorti is no more a stone. It is the deity in person.
Usually temples are open most of the time of any day. One could go individually or in groups any time. On some holy days, celebrations occur at the temples, then a large mass of people gather and participate.
Last month a Christian university invited me to give an educational talk on the Hindu dharma. They had given me two hours. They kept listing me for more than 3-hours, and still they were interested to know more. So, if any group/church you know has friendly interest to know the Vedic dharma as it is in the scriptures let me know. I will be pleased to come and talk. We do not share info about dharma with those who hate it.
Hope this helps you.
Jai Sri Krishna!