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Hi Sally. It sounds like there may have been some rosebushes planted there at one time. The top part of the bushes died most likely so folks either dug them out or just cut them way down and placed dirt over them. The roots from the hardy root stock are still trying to survive so they send up little rose shoots here and there. Some of these will never bloom, others may bloom eventually with large flat deep red blooms or pink blooms. However these root stock survivors can become very vigorous and totally take over the garden areas they are in, so be careful in letting them grow if that is what you decide to do.

Yes you can if you have plenty of sun and warm weather.

Those would be rose hips or the fruit of the rose. Neat to see them and especially pretty in winter snows. Article Link: https://www.gardeningknowhow.com/ornamental/flowers/roses/rose-hip-information.htm

Not all wild roses are desirable. One that can just show up is the invasive multiflora rose; this you absolutely do not want and removal is advised. Stems quickly grow long and arching and thorns are large. It blooms once in spring. Another surprise rose is Rosa rugosa "beach rose". This spreads slowly by underground stolons and will form a colony in 10 years. Of course, you can remove unwanted new plants. Rose hips are nice on beach rose. They bloom all summer but not with the big flush of blooms seen in hybrid roses. There are native wild roses and these flower with dainty, simply blooms. They are usually under 3 ft tall. Their open flower makes it easier for pollinators to reach nectar and pollen. If you send a photo we might be able to recognize which one you have. Being in bloom helps.