Are fragments with the same number of base pairs always the same exact fragment?

No, the fragments with same number of base pairs  do not always the same exact fragments.

Lets take an example, There are two fragments of DNA, having 20 number of base pair each. But the one fragment contains a sequence in which there are 12 GC base pairs.

The second fragment contains sequence with only 5 GC pairs.

Hence the same number of base pairs in fragments does not assure Exact fragments.

relative dating involves things like higher layers are most recent than rocks lower in the sequence. this can be extended to the known sequence of fossils. rocks containing rabbit fossils are later than those containing dinosaur fossils.  

absolute dating methods mainly use radioactive elements that have known rates of decay and produce recognizable products. for example potassium 40 decays to produce argon. once a rock has solidified the argon is trapped. by measuring the argon and potassium0 you can get an accurate number for the age.  

some other methods are good for archaeological ages. dendrochronology involves recognizing the sequence of tree rings. the orientation of magnetized particles in baked clay can be used to date a fire.

hope this .. .