Can I grow these plants indoors?
You can try, but you need to provide enough sunlight for them. This can be difficult for full sun plants like these. If you have a sunroom or atrium, you should be fine, but otherwise, it could be difficult to provide that.
I live in Central Ohio. I ordered Dicliptera [jacobinia] suberecta in early July but did not get until August. It's now September 11 and I'm thinking it's too late to plant outside, but can I plant and keep indoors until next spring. The plants are approx. 3" tall, so very tender.
Yes you are right about protecting it for the winter. Your climate is too cold to grow this species outdoors year round as a perennial, so as the following article suggests, you can grow it as an annual. To keep it inside for the winter, give it as much light as possible, a south facing window if you can. Let the soil dry out between waterings. As small as it is, I think it will make it.
https://www.gardeningknowhow.com/ornamental/flowers/hummingbird-plant/growing-hummingbird-plants.htm
You state to mark the north side of the plant. Which way should the plant face when transplanting? North, south, east or west? I am in zone 9A.
It can face however it looks best. I believe tying yarn to the northern branch tip is only so your shrub will be sitting straight up in the new hole. I take it to mean the top of the shrub, not facing a certain way. Sometimes with shrubs its hard to get them upright in the new planting hole. They look like they are leaning on one side.
https://www.gardeningknowhow.com/ornamental/shrubs/firebush/how-to-transplant-a-firebush.htm