In general, common judgment is the most important factor. Always reference situation to similar thing or situation in real-life or in book or movie. Not all decisions must be completely realistic and equal, the most important thing is flexible, fast and smooth gaming. This is a game where no common things are tested. If the character is skilled in lock-picking, he should succeed in that unless the situation is a very special one.
Comparison levels: Althought RIP does not have pre-defined tests and rolls, it does have skill and attribute levels. These levels are used to give the gamemaster and players some values to compare. Thus, if some character has horse riding 1 (skilled) and the other 2 (expert), you know that the later one is better in horse riding. Similarily, if the character has that horse riding skill you know that he can ride a horse at some degree. And in even hand-to-hand combat, the character with higher melee skill is going to win unless the other character somehow succeeds to surprise the opponent. Of course if the combat is not even (the other character has longer reach, better equipment, is much stronger or faster etc.) then the situation is completely different.
But how well does a skilled horse rider ride? Can he make the horse leap over obstacles and keep on saddle? Can he shoot while the horse is galloping? These things are a bit hard to pre-determine in the game system, as it is also dependant on what the character has learned while taking horse riding lessons. The skills in RIP are so broad that they cannot handle each tiny subsection of the skill - maybe the other rider has concentrated on making the horse jump while the other can do tricks while on the saddle. When questions like this arise, players are encouraged to add specializations and training notes to skills (see characters).
Thus, there is no exact way to determine if the character stays in the saddle. The task of the gamemaster is to tell the player the odds (not real numbers but like 'you are almost sure you can do that' or 'maybe you succeed but then you are lucky') and the player can then tell if the character tries the trick. Then some dice can be rolled, like a d6 roll and a roll 1 is a failure if the trick is quite easy but there is possibility to fail - the gamemaster or the player rolls the die and then the gamemaster interprets the result. Naturally this means that if the same feat is repeated later on, the exact roll might be different. But it is very rare that the situation would be exactly the same, either.
Now you can think that it is unfair that the exact system is not known. But how many of us can tell the exact probablities to succeed in something if you try that in the real life? In similar way, why should the players know the exact probablities in the game.
Bad luck die: Althought dice rolls are not encouraged to all kind of common tasks, like skilled character doing something he is skilled at, most of the time some suspension is needed and especially when the situation is a stressful one, the character can fail, despite all the training. One way to handle this is to roll one single d6 each time something very crucial is tried. If the die ends up as 1, it means that not everything went well and a new die is rolled to see how bad it went. This does not mean that characters should fumble 1/6 of the time, but instead a roll of 1 can mean like some extra time or perhaps call for some kind of Willpower test. A fumble could be something like three or more subsequent 1's rolled.
This bad luck dice can be something not even tied to skill levels of the character! For example, the character is picking a lock in an empty hallway. The gamemaster rolls a d6 and 1 is rolled - now something unexpected happens and the gamemaster rerolls the die to see how bad is that. A 5 is rolled, so the gamemaster decides that the character hears footsteps closing.. now the player must decide does the character keep on trying to pick the lock (with possible Willpower test to keep the concentration despite the closing footsteps) or do some other action.
In any case, the most determining factor is the description given by the players of their characters' actions. This can be a bit unfair to players who cannot picture the situation nor have any experience in such events, and thus in most cases the skill levels of the character should be sufficient.
In melee combat, main factors come from weapons used, skill of the combatants and locations in the combat. Thus, the participant with better position (upper ground, familiar location, better sight etc.), longer reach or just faster has extra advantage. Or if the melee becomes a brawl, the stronger and heavier one is going to rule, even if the other one is a bit better at boxing, for example.
In ranged combat, use the situation. In most cases, it is quite hard to hit someone which is moving, especially if that move is irregular. Similarily, trying to hit something while not aiming or while moving makes things very hard if not impossible.
Likewise, an armor or other object may have ballistic protection, shortly as BP. This value tells how concentrated hits the armor can still stop by expanding the force around larger area.
Against concussion damage, armor or creature may have padding. This padding is directly reduced from the general attack strength, unless the armor is penetrated.
If the attack penetrates the armor, a shock wave and expanding bullet usually do massive damage, causing severe blood loss. A limb hit becomes easily defunctional, a hit to torso causes dangerous internal bleed fatal in hour or some days, and head hit is usually immediately fatal or at least causes unconsciousness and death within day in hospital. Even if the bullet does not expand (armor piercing), it may penetrate vital organs and cause death in minutes or hours from internal bleed.
No armor penetration is ever tested with simple concussion attacks. Just reduce possible padding from attack strength, and determine effects of the final damage. 2 or more points may snap little bones or cause internal bleed, while 5 or more points usually do very extensive damage.
Non-human races might have completely different rules.
A week or two is required for small cuts to fully close and little breaks to heal. A month or two is required for more severe breaks. Good rest and nutrition is essential for healing.
Lost limbs or organs do not regenerate.
These rules are for humans, non-human races might have complete different healing metabolism. Similarily any healing magic, advanced drugs and medical systems can modify these rules.