Surenlicious, I will address your two questions separately, starting with bone splinters in the bloodstream.
What you are describing is a foreign body embolism and they only occur due to medical errors or complications. I actually did a bit of research about this topic by trying to find case studies of bone splinters entering the blood stream just to be double sure that this literally never happens. Comminuted fractures which produce lose splinters of bone are still stabilized by a ton of connective tissue, basically immobilizing fragments in place. Although we have blood vessels basically everywhere, most are too small to carry something as big as a bone fragment. I thought for a second that maybe a comminuted fracture shattering the clavicle might puncture the superior vena cava or aorta which are a big enough vessels to carry bone fragments, but I have couldn't find any case reports of this ever happening and you would bleed out from puncturing one of those vessels before anyone could do anything for you. Survival rate for people with aortic dissection (or a tear in the aorta) is 10% if treated. So yeah, not survivable outside the hospital setting really.
Regardless, of whether bone splinters enter the bloodstream or not, fractures to long bones still can cause embolisms, just not foreign body embolisms. So lets talk about embolisms for a minute, because the outcome of them will be the same no matter what the substance is that caused the embolism.
Simply put an embolism is something not dissolved in the blood traveling in the blood stream. The most common form of an embolism is made out of coagulated blood and cells clumped together. This is called a clot and is the leading cause of heart attack and stroke. As already mentioned, an embolism can also be made out of a foreign body from a broken medical device such as an IV. You can even have an air embolism. The symptoms for all types of embolisms are pretty similar, but the type that is caused by fractures of the long bones (femur, tibia, ulnar, humerus) is called a fat embolism.
Merrow from the center of fractured long bones can leak into the bloodstream and collect to form fat embolisms. These are actually super common after fracture, but usually dissolve on their own without ever causing any symptoms. If the embolism is big enough it will travel to very small blood vessels, called capillaries which are only one cell thick. There the embolism will eventually get lodged and cause symptoms. What symptoms occur depends upon where the embolism gets lodged.
The most common location for a fat embolism to lodge is in small blood vessels of the lungs. When this occurs, it is called a pulmonary embolism and is extremely deadly. Basically it obstructs blood flow to the lungs so you cannot exchange carbon dioxide for oxygen. Patients will cough up pink (blood) frothy sputum, feel short of breath, have sharp chest pain, sweat, and quickly deteriorate due to lack of oxygen.
Low oxygen content in the blood is called hypoxemia and affects all organ systems simultaneously. At first, the body will try to compensate by pumping more blood to the body or trying to force more air into the lungs. Your breathing will deepen and quicken and your heart rate will speed up. The body will also shunt blood away from nonvital areas of the body (like your limbs, skin, and even kidneys and other abdominal organs) towards vital parts (like the heart and brain). This is why people with hypoxemia will turn bluish grey and have acute kidney injuries after they recover.
However, without gas exchange happening in the lungs and hence oxygen making it into the blood, this is not sustainable and patients quickly tire out. They may become unconscious due to lack of oxygen to the brain. The heart will become inflamed and damaged due to lack of oxygen. When damage is so severe that it interrupts the electrical signaling pathways that tell the heart to beat, it's endgame. The heart stops pumping effectively and eventually stops altogether.
I've literally seen patient's die from pulmonary embolisms within 30 minutes from the time they first told me they were feeling pain and having difficulty breathing. The only treatment for this is quick recognition and removal of embolism by catheterization in the hospital. There is no "in the field" or "medieval" substitute for this treatment. Anything else you try to do to remove the embolism will just make it worse.
The second most common place for an embolism to lodge is in the brain. When an embolism lodges there it causes a stroke, which is basically lack of blood flow or oxygen to the brain. What symptoms a patient may have will depend on where exactly in brain the embolism ended up. People may have motor, sensory, speech, or intellect deficits. Their personality may change, usually becoming more impulsive and less able to reason logically. All these problems may improve with therapy or may be permeant.
If an embolism lodges anywhere else in the body, it is not usually a problem and you won't even notice that it happened before it is dissolved. Heart attacks are also caused by embolisms (this time getting lodged in the vessels of the heart), but they are almost always caused by clots, not fat embolisms, for complex anatomy reasons I won't get into, because it's not relevant to your story.
Anyways, hope this answers your first question! Just remember, although sharp, pointy bone fragments won't make their into the bloodstream through any means besides magical or scifi mumbo jumbo, bone components (i.e. marrow) will! Also, embolisms of any size (which by definition is anything larger than a red blood cell) will eventually lodge somewhere, so if you are going for the "I've got metal traveling in my blood stream like a terminator boss", it's not feasible. Embolisms either go away on their own or cause serious health issues very quickly. No in-between.