Yes, they need to be repaired so you get a nice smooth looking surface. Here is a link to nail pops. It will give you step by step instructions. https://www.mrhandyman.com/tips-ideas/drywall-walls/how-to-repair-nail-pops/   There are a few ways to repair the drywall tape, and you can look up a u tube video for instruction. I always remove the tape and start fresh. If you are unsure about this, you can hire a drywall man to come in and do it for you, and it shouldnt be a huge expense. You sound like you might be inexperienced in this type of thing, and ceiling joints are maybe not the place for you to learn. I would however, watch the repair person carefully, so next time, you might want to do it yourself.

Paraphrasing Mark Twain, "It was built in the 90s and clearly cheaply done. But I repeat myself."

Unfortunately true. (Original here.) I've seen lots of what you describe in homes built from about 1970 on.

I tackled the exact same problems in a relative's house finished in the late 1990s. I won't say that I'm an expert or that mine was/is the best way, but it held up for the year or so longer that she lived there.

The popped nails I reset with a few taps from a ball peen hammer. (You want to be careful not to drive them in so deep that they break the drywall's surface paper.) Then I mudded them over, sanded, primed, and painted.

For the lifted tape, I stuffed mud under the loose edges with a drywall knife, pressed it down smooth with the knife, then mudded it over. Same as with the nails - sanded, primed, painted.

@Cat_ky I’m definitely not experienced in fixing these issues, but as we’ve learned to frame out walls, put in support beams, level floors, move exterior doors, replace windows, install cabinets, put in hardwood floors, move HVAC (although that did take some help from an HVAC prof), and more with this house, I’m willing to give it a shot on my own ;)

(Before my statement sounds alarming to anyone- we did have professional guidance and oversight from family and friends in the business, but 90% of the work has been on our own.)

Thank you both, I’m going to tackle these issues this weekend!

Let us know how everything works out. I am betting you can do it. :-)