I am so much confused about several things of the special relativity.
First, in the flat spacetime, are the available frames of reference all inertial frames? I think that because inertial frames are defined as frames without gravity and the flat spacetime is not curved, the frames of reference for the flat spacetime must all be inertial. Am I correct?
Second, are all inertial frames of reference connected by Lorentz transformations? I cannot find a way to connect an inertial frame 'translated' by a fixed amount from another inertial frame by Lorentz transformations. If there exist inertial frames that are not connected by Lorentz transformations, then is it possible to guarantee that physics law does not depend on coordinates?
Third, in special relativity, the force and acceleration are handled in a given inertial frame. However, then, how should I deal with the frame of the particle that is accelerating in the structure of special relativity? The accelerating particle's frame is certainly not inertial...
I am extremely confused and frustrated due to the questions above. Could anyone please help me...?