##05AB1E, 20 13 12 bytes##

A.p¦«vy¦«,

Explanation

A.p          # push all prefixes of alphabet
   ¦«       # concatenate each with it's reverse minus the first char
      v      # for each string:
       y¦«  # concatenate with it's reverse minus the first char
           , # print with newline

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05AB1E, 20 13 12 6 bytes

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Saved 6 bytes thanks to Magic Octopus Urn and some new language functionality.

Aη€ûû»

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Explanation

Aη       # push prefixes of alphabet
  €û     # palendromize each prefix
    û    # palendromize the whole list
     »   # join on newlines

##05AB1E, 20 13 12 bytes##

A.p¦«vy¦«,

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Saved 2 bytes thanks to Adnan.

##05AB1E, 20 13 12 bytes##

A.p¦«vy¦«,

Explanation

A.p          # push all prefixes of alphabet
   ¦«       # concatenate each with it's reverse minus the first char
      v      # for each string:
       y¦«  # concatenate with it's reverse minus the first char
           , # print with newline

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##05AB1E, 20 13 bytes##

A.pvy¦«=}gF,

Explanation

A.pv     }     # for each prefix of the alphabet
    y         # bifurcate (push it and it's reverse)
      ¦«       # remove first char of the reversed string and concatenate
        =      # print while leaving on the stack
          g    # length of top item (the longest string)
           F,  # pop and print that many times (prints the lines of decreasing length)

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##05AB1E, 20 13 12 bytes##

A.p¦«vy¦«,

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Saved 2 bytes thanks to Adnan.