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Usually anywhere from 8-12 inch spacing but you can plant them closer if you want. This article should help: https://www.gardeningknowhow.com/ornamental/flowers/impatiens/growing-impatiens-flowers.htm

Looks like it might be Impatiens balsamina. AKA garden balsam, garden jewelweed, rose balsam, touch-me-not.

Are you noticing any white coating on the plants as well? I ask because these plants are very susceptible to downy mildew, especially in your area. It also overwinters in the soil, which would explain why it happens each year. Here is more information: https://www.gardeningknowhow.com/ornamental/flowers/impatiens/impatiens-downy-mildew.htm

It is generally difficult to keep impatiens plants over winter. You can try giving the plant plenty of light and warmth, but you may want to consider taking some cuttings instead to ensure you will have more of the plant in the event that they do not survive over winter (since they are annuals). This article will help with that: https://www.gardeningknowhow.com/ornamental/flowers/impatiens/impatiens-rooting.htm

That would be scale. This article will give you some ideas on treatment: https://www.gardeningknowhow.com/plant-problems/pests/insects/control-plant-scale.htm

If your purchasing plants from a reputable nursery or garden center, they should be able to inform you about the health of the plants they are selling.
Plants can appear healthy at purchase but become susceptible to the air born fungus downy mildew.
Many growers are producing impatient varieties that are resistant to disease. If you love the plant it may be worth searching out these varieties.
If your unsure of the health of the plants I would choose another shade loving annual to enjoy.

http://www.dispatch.com/content/stories/home_and_garden/2015/01/18/1-mildew-resistant-impatiens-among-notable-2015-all-america-offerings.html
https://www.gardeningknowhow.com/plant-problems/disease/downy-mildew.htm
http://negreenhouseupdate.info/updates/impatiens-downy-mildew-update-0