My question is fairly simple, i.e., do all beings in this world "get reborn" through karma, or are there ascended beings in this world, living as human beings, free of all suffering?
It is correct, that beings get reborned due to their kamma. Kamma means action, but not just any action. The type we are talking about here is volitional action, i.e. actions where intentionality is present. This type of action is kamically potent. Kamma is created by body, speech and mind. It originates from the Mind and is based in either wholesome or unwholesome roots. Volitional actions have consequences, we call that vipakka which means "ripening" or phala (fruits).
The ripening need not to come right away, i.e. in this life. It can also come in the next life or operate across the succession of lifetimes. If you are interested in reading more about kamma and rebirth, references by Ven. Bhikkhu Bodhi, can be found here.
There are beings in this world that are free some suffering, i.e. Arahants and possibly Pacceka Buddhas (silent Buddhas). These Buddhas are self-enlightened and arise between the time of two fully enlightened Buddhas, e.g. our Buddha, Gautama and the next Buddha to be, Maitreya.
If you would like to read more about Arahants, Pacceka Buddhas and Buddhas, Ven. Yuttadhammo has written about all of them in this answer.