If I'm in outer space, and suddenly start accelerating, will I feel it? If I'm in outer space, initially at rest, and every single particle in my body accelerates at the same rate in the same direction, will I feel that? My brain is fried thinking about this. There are two possibilities:

*

*initially at rest and then accelerating with const acceleration w.r.t. some inertial frame, and

*initially at rest and then accelerating with const acceleration w.r.t. some non-inertial frame

So will I feel anything:

*

*while I'm in motion

*when I transition from a state of rest to a state in motion

My intuition is that I shouldn't feel anything in any of the scenarios (every single particle in my body accelerates at the same rate - so there's no source of tension- any kind of push or pull- between various parts of my body), but I could be very wrong.
 A: Yes. Via the equivalence principle if you accelerate with respect to a locally inertial reference frame, then you will not be able to distinguish the effects of acceleration from a gravitational field. So you will effectively feel a gravitational force acting in the direction of acceleration, with a magnitude proportional to the magnitude of the acceleration.

Note added due to discussion in the comments.
There's a contradiction implicit in the question. If you are truly isolated in empty space, then you can't be accelerating (you must be in a locally inertial reference frame), because of Newton's first law. So there's two strategies to answer this question:
(a) point out the contradiction and leave it at that (which is kind of a boring answer), or
(b) assume that you are accelerating but then also assume there is something causing the acceleration.
I'm taking approach (b) in my answer (although by adding this note I have also addressed point (a)).
Another key point that came up in the comments, is that a locally inertial frame is also a freely falling frame. (Here I am working in the framework of General Relativity, which is the most accurate description of gravity we currently have). So a freely falling observer is not accelerating relative to a locally inertial frame, and does not experience a force.
A: The physics answer is, an accelerometer will detect all accelerations relative to an inertial frame. If you're in free fall being accelerated by a gravitational field, the answer is actually no, because a frame in free fall is inertial, even though for most purposes it's more useful to treat it as an accelerating frame.
So to your questions in order,
1a Yes, but free fall counts as inertial.
2a Only if you are also accelerating w/r/t an inertial frame.
1b No, if by "while I'm in motion" you mean constant velocity.
2b Yes, subject to the above.
The engineering/biology answer is flat "No." You specified that every part of you is being identically accelerated, and if that's the case, there's no way for an accelerometer (biological or otherwise) to be designed such that it will detect any acceleration. An accelerometer works by measuring the difference in motion between a mostly-inertial frame (like a mass on a spring, or fluid in your inner ear) and the accelerating frame (the body of the accelerometer, or your skull). If every particle is identically accelerating, there's nothing to measure.
A: No. Let's consider the case where you're out floating in free space, and suddenly a large moon pops into existence in your vicinity, which you start accelerating toward due to gravity.
Before the moon appears, you're obviously in an inertial frame.
After the moon appears, you're in free-fall toward it, which is also an inertial frame. See the equivalence principle:

Objects in free-fall do not experience being accelerated downward (e.g. toward the earth or other massive body) but rather weightlessness and no acceleration

Any two inertial frames are experienced equivalently; you could not distinguish transitioning from one to the other.
A: No. Since every particle in your body accelerates at the same rate, there are no forces between them and no compression or tension. This is identical to being in freefall in a gravitational field. An astronaut in orbit, for example, is affected by the force of gravity at all times, but doesn't "feel" anything because they are in free fall. Half an orbit later, the astronaut is accelerating in the exact opposite direction, but it doesn't feel any different. At no point can the astronaut determine that they're in one half of the orbit versus the other, or just floating in deep space far from any mass and not in orbit at all. In all cases, they're simply accelerated by the local gravitational field, which always feels the same - like no acceleration at all.
Humans only feel proper acceleration, which is acceleration that deviates from the local gravitational field. Humans do not feel coordinate acceleration, which is acceleration with respect to some fixed point (and will vary based on the fixed point). Your unseen force is acting on every particle in your body exactly the way a gravitational field would. Since you can't feel the acceleration due to a gravitational field when in freefall, you can't feel the acceleration due to this force that operates in the exact same way.
See also: Would an astronaut experience a force during a gravity assist maneuver?
A: Just what exactly is "constant acceleration" in relativity is a bit more complicated that it might seem at first. If, relative to a fixed reference frame, your change in velocity per unit time is constant, that at some point you will exceed the speed of light. So that type of acceleration is physically impossible in the long term, but in the short term it would be possible. However, if you are accelerating at a constant rate relative to some fixed frame of reference, then since your time is slowing down relative to that frame of reference, your acceleration will be increasing in your frame of reference.
We can also consider an object experiencing constant proper acceleration; that is, the acceleration relative to its instantaneous frame of reference is constant. This can be characterized by Rindler coordinates, but in Rindler coordinates an object of finite length will have to have different accelerations at different points.
A: You've stumbled upon the difference between body forces and surface forces.  Body forces act directly on the entire body of an object, while surface forces act directly only on the surface of an object.  When you sit in a chair, the direct force you feel is the chair pressing against your bottom.  You don't feel the chair throughout your whole body, because it's only acting on the surface.  Gravity, however, is a body force.  In your everyday life, you can't really feel it directly because it acts almost* evenly on your entire body.  You can feel the fluid in your inner ear flow around, or your feet pressing against the floor, but you can't actually feel gravity itself.
*There are tidal forces caused by gravity being weaker higher up, but on Earth these are many orders of magnitude too small to feel.
