Gravity and velocity increase and time effects problem First I must specify I am a math major and not currently taking any classes on physics and this is a casual interest/hobby of mine.   Therefore I apologize in advance if my questions seem naive.
An object sits near a gravitational well. The object begins to accelerate toward the center of the gravity well.
There exists a reference frame outside which sees this object falling in.
The object itself is said to experience time at a slower rate as the gravity increases.
Query: Does the object experience time slower itself or is the time dilation only measurable and therefore visible to an outside reference frame but not known to the object experiencing said dilation? i.e., it's life expectancy is some arbitrary time and it lives that time according to it's own clock but to an outside observer it lives much longer. 
Now let us state this object, call it particle A, is moving at 99.999% of c.
It is being followed by the outside reference frame at the same speed from a separate entity.
 Call these, two particles: Particle A: the one which will intersect a black hole or some sufficiently large gravity well, and Particle B travels at the same velocity parallel to particle A but far enough away that it can observe particle A's interaction with the gravity well without being a part of the gravitational interaction.        
Query: Let us assume for a moment that an object can actually reach the limit of the speed of light for it's velocity. Particle A is said to to be moving so close to C that a sufficiently large gravitational well should give it the boost necessary to reach that limit as it falls in or approaches. Since Particle A should be experiencing time at a slower rate. What does particle B see in this scenario without worrying about the particles frame slowing down, etc.? 
The first question is of the most importance to myself.
-Thank you for your help.
 A: To your first question-
The particle falling in seems to move slower with respect to an observer at rest outside.The word observer is the most important as it denotes the reference frame.The object falling in the gravitation well is in the same frame as its clock.So,all things move slowly for it,including its biological clocks(heart,pulse,etc.) and its brain.So, the object itself cannot perceive any slow down in its environment.But to an outside observer the whole system of the falling body is moving a t a slower rate.So,to him it appears that his time is dilated.And as for increase in life expectancy it also varies from observer to observer with change in reference frames.To the outside observer as in this case,the life expectancy of the falling man increases as its biological clocks move slower with respect to him. For example imagine the life time of a man is for 50,000 beats of the heart.Now with slow down of the heart beat rate it takes a longer time to complete 50,000 beats and thus the life expectancy appears to increase.But remember the most important thing here-from observer to observer and reference frame to reference frame it varies.
