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Explore Stack Internal #Python, 453 363 bytes
s,n=input() o="""ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz&_?!"'.,""" p="""∀qƆpƎℲפHIſʞ˥WNOԀQɹS┴∩ΛMX⅄Zɐqɔpǝɟƃɥᴉɾʞlɯuodbɹsʇnʌʍxʎz⅋‾¿¡„,˙'""".decode('utf8') s=map(''.join,zip(*[iter(s+' '*(n-1))]*n)) for i in range(len(s)): if i%2:s[i]=''.join(p[o.find(c)].encode('utf8')for c in s[i][::-1]) for l in s:print l #Python, 453 363 bytes
s,n=input() o="""ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz&_?!"'.,""" p="""∀qƆpƎℲפHIſʞ˥WNOԀQɹS┴∩ΛMX⅄Zɐqɔpǝɟƃɥᴉɾʞlɯuodbɹsʇnʌʍxʎz⅋‾¿¡„,˙'""".decode('utf8') s=map(''.join,zip(*[iter(s+' '*(n-1))]*n)) for i in range(len(s)): if i%2:s[i]=''.join(p[o.find(c)].encode('utf8')for c in s[i][::-1]) for l in s:print l s,n=input() o="""ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz&_?!"'.,""" p="""∀qƆpƎℲפHIſʞ˥WNOԀQɹS┴∩ΛMX⅄Zɐqɔpǝɟƃɥᴉɾʞlɯuodbɹsʇnʌʍxʎz⅋‾¿¡„,˙'""".decode('utf8') s=map(''.join,zip(*[iter(s+' '*(n-1))]*n)) for i in range(len(s)): if i%2:s[i]=''.join(p[o.find(c)].encode('utf8')for c in s[i][::-1]) for l in s:print l #Python, 453453 363 bytes
d=dict(zip("ACEFGJKLPRTUVYacefghijkmrtvwy&_\".", map(unichrs,n=input(8704,390,398,8498,1508,383,670,741,1280,633,9524,8745,923,8516,592,596,477,607,387,613,7433,638,670,623,633,647,652,653,654,8523,8254,8222,729)))) d.update(dict(zip("BDHIMNOQSWXZbdlnopqsuxz',!o="""ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz&_? ",u"qpHIWNOQSMXZqpluodbsnxz!"'.,'¡¿ ")))""" sp="""∀qƆpƎℲפHIſʞ˥WNOԀQɹS┴∩ΛMX⅄Zɐqɔpǝɟƃɥᴉɾʞlɯuodbɹsʇnʌʍxʎz⅋‾¿¡„,n=input˙'""".decode('utf8') s=map(''.join, zip(*[iter(s+' '*(n-1))]*n)) for i in range(len(s)): if i%2:s[i]=''.join(d[c]forp[o.find(c)].encode('utf8')for c in s[i][::-1]) for l in s:print l.encode('utf8') #Python, 453 bytes
d=dict(zip("ACEFGJKLPRTUVYacefghijkmrtvwy&_\".", map(unichr,(8704,390,398,8498,1508,383,670,741,1280,633,9524,8745,923,8516,592,596,477,607,387,613,7433,638,670,623,633,647,652,653,654,8523,8254,8222,729)))) d.update(dict(zip("BDHIMNOQSWXZbdlnopqsuxz',!? ",u"qpHIWNOQSMXZqpluodbsnxz,'¡¿ "))) s,n=input() s=map(''.join, zip(*[iter(s+' '*(n-1))]*n)) for i in range(len(s)): if i%2:s[i]=''.join(d[c]for c in s[i][::-1]) for l in s:print l.encode('utf8') #Python, 453 363 bytes
s,n=input() o="""ABCDEFGHIJKLMNOPQRSTUVWXYZabcdefghijklmnopqrstuvwxyz&_?!"'.,""" p="""∀qƆpƎℲפHIſʞ˥WNOԀQɹS┴∩ΛMX⅄Zɐqɔpǝɟƃɥᴉɾʞlɯuodbɹsʇnʌʍxʎz⅋‾¿¡„,˙'""".decode('utf8') s=map(''.join,zip(*[iter(s+' '*(n-1))]*n)) for i in range(len(s)): if i%2:s[i]=''.join(p[o.find(c)].encode('utf8')for c in s[i][::-1]) for l in s:print l #Python, 453 bytes
d=dict(zip("ACEFGJKLPRTUVYacefghijkmrtvwy&_\".", map(unichr,(8704,390,398,8498,1508,383,670,741,1280,633,9524,8745,923,8516,592,596,477,607,387,613,7433,638,670,623,633,647,652,653,654,8523,8254,8222,729)))) d.update(dict(zip("BDHIMNOQSWXZbdlnopqsuxz',!? ",u"qpHIWNOQSMXZqpluodbsnxz,'¡¿ "))) s,n=input() s=map(''.join, zip(*[iter(s+' '*(n-1))]*n)) for i in range(len(s)): if i%2:s[i]=''.join(d[c]for c in s[i][::-1]) for l in s:print l.encode('utf8')