The Epigraph at the beginning of the Prologue says "He shall bear the weight of the world on his arms". This is exactly what Sazed does in Hero of Ages when taking up Preservation and Ruin to Ascend to Harmony.
You are correct in assuming Adonalsium was a being, or a force. Many people in the cosmere worshipped it as a god (indeed, it's name comes from the Hebrew word Adonai, the name of God). In Cosmere prehistory, Adonalsium was split into sixteen Shards with varying Intents, each attribute coming from a different part of that god's behavior, aspects, or motives. The sixteen people that managed to kill Adonalsium then took up those Shards and thus was born the Cosmere as we know it. We don't know for sure how any of this transpired, but there are theories.
We don't know for sure if Adonalsium had a Vessel or not.
The leading theory is that if you combined all the Shards, it would lead to the restoration of Adonalsium. In fact, that is one of the big questions in the Cosmere, that certain background characters may be trying to bring about behind the scenes over many years. We don't know for sure if it would happen this way, or if Adonalsium would even be the same being, but there is a lot of evidence to support the theory.
The Seventeenth Shard is an in-universe organization that is interested in keeping the Shards separate. They figure that Adonalsium was killed for a reason, and we should let it be. They also seem mostly well-intentioned, as they don't want any planets to be destroyed (which is nice), but they also have a "Prime Directive" type aspect to them, not wanting to get too involved in individual planets' problems. We took the name because it's cool, and something in universe that we don't know much about yet.
Hope that helped! Enjoy the Cosmere.
A relevant quote on Soulstamping from the Chicago signing in December:
Source. (Scroll down to page 16)
I underlined the part about Knights Radiant, but the rest is good to know too. On your first question, that's most likely correct, she would probably heal herself in the pattern of her overwritten stamps. On the second one, it's hypothetically possible, but it would take so much Investiture that it wouldn't be worth it.
Khyrindor's post in Mistborn Ending was marked as the answer