I assume you got two basic versions of shapeshifting

One is in name, it just simply shifts your shape, nothing else.

The other is physically altering your body's appearance to look like on the outside as the person you are disguising yourself as, not genetically or physically, only visually.

Hm...

Very intriguing question. I never thought of shapeshifting like this but, the answer to your question might be in what you said you are correct about the cellular manipulation part it wouldn't make sense. Unless your ability to shapeshift is caused by something like Beast Boy for example when he transforms he is still green due to the serum side effects. This leads us to psionic / magic I like to think that if you are shapeshifting it is like you molding your body into what you're transforming to kind of like a puppeteer playing with a puppet but the puppet is your body while the puppeteer is either your soul, Astral form, or magic in a sense. To dive deeper though you might have to determine the limitation of such power first before you can determine where the shapeshifter lies. Also to answer your other questions yes they should be able to remove, modify, or add memories/personalities to themselves don't know why they would but it is entirely possible, and yes an inexperience shapeshifter could possibly kill themselves from either strain, lack of control, or even trying to do something beyond their limits.

Sorry its lengthy

@OrionEion