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This is normally indicative of stress realted to its new environment. Generally, this fixes itself over time but you may need additional light or humidity to fix it. Here is an article that you may find helpful: https://www.gardeningknowhow.com/houseplants/ferns-houseplants/growing-ferns-indoors.htm

This typically happens when the plant is not getting enough light. If you can, move it to a brighter location, but remember that the light needs to be filtered. If this is not possible, try to get supplemental light, like a florescent light, near it.

Yes, if it's root bound to the point that its roots cannot breathe, you definitely need to transplant the fern to another larger pot. You should also root prune the plant. These articles will help: https://www.gardeningknowhow.com/ornamental/foliage/asparagus-fern/asparagus-fern-care.htm, https://www.gardeningknowhow.com/houseplants/hpgen/prune-roots.htm As for the egg-like things, if these are orange to brown protrusions along the underside of the plant fronds, they are likely only spores and perfectly normal. On the other hand, nearly flat brown oval spots can indicate scale bugs and white or clear-looking sacs on the plant are indeed eggs left behind from a pest. After repotting your fern, treat the plant with neem oil, which should take care of any insect pest that may be affecting your plant but will not affect the spores (if this is actually what you are seeing). Here is more information: https://www.gardeningknowhow.com/problems/pests/neem-oil-uses.htm

This article should help: https://www.gardeningknowhow.com/edible/vegetables/asparagus/cutting-asparagus-foliage-back-in-autumn.htm

This looks like an asparagus fern.
http://pics.davesgarden.com/pics/2007/04/09/Gabrielle/1afda6.jpg

Here is a link to help you.

https://www.gardeningknowhow.com/plant-problems/pests/insects/kill-wasps.htm