Python: 504 519 chars
(Python 3 solution) Currently requires to set the input in the format as shown at the top (input code is not counted). I'll expand to read from file or stdin later. Now works with a prompt, just paste the input in (8 lines total).
R=range
f,p=[input()[1:11]for i in R(7)],p
for(a,b)in input().split():
t=[' '*int(b)+r+' '*9for r in{'I':'#,#,#,#','O':'##,##','Z':'##, ##','T':'###, # ','L':'#,#,##','S':' ##,##','J':' #, #,##'}[a].split(',')]
for r in R(6-len(t),0,-1):
for i in R(len(t)):
if any(a==b=='#'for(a,b)in zip(t[i],f[r+i])):break
else:
for i in R(0,len(t)):
f[r+i]=''.join(a if b!='#'else b for(a,b)in zip(t[i],f[r+i]))
if f[r+i]=='#'*10:del f[r+i];f[0:0]=[' '*10];p+=10
break
print('\n'.join('['+r+']'for r in f[:7]),p,sep='\n')
Not sure if I can save much more there. Quite a lot characters are lost from the transformation to bitfields, but that saves a lot more characters than working with the strings. Also I'm not sure if I can remove more whitespace there, but I'll try it later.
Won't be able to reduce it much more; after having the bitfield-based solution, I transitioned back to strings, as I found a way to compress it more (saved 8 characters over the bitfield!). But given that I forgot to include the L and had an error with the points inside, my character count only goes up sigh... Maybe I find something later to compress it a bit more, but I think I'm near the end. For the original and commented code see below:
Original version:
field = [ input()[1:11] for i in range(7) ] + [ 0, input() ]
# harcoded tetrominoes
tetrominoes = {'I':('#','#','#','#'),'O':('##','##'),'Z':('##',' ##'),'T':('###',' # '),'L':('#','#','##'),'S':(' ##','##'),'J':(' #',' #','##')}
for ( f, c ) in field[8].split():
# shift tetromino to the correct column
tetromino = [ ' ' * int(c) + r + ' ' * 9 for r in tetrominoes[f] ]
# find the correct row to insert
for r in range( 6 - len( tetromino ), 0, -1 ):
for i in range( len( tetromino ) ):
if any( a == b == '#' for (a,b) in zip( tetromino[i], field[r+i] ) ):
# skip the row if some pieces overlap
break
else:
# didn't break, insert the tetromino
for i in range( 0, len( tetromino ) ):
# merge the tetromino with the field
field[r+i] = ''.join( a if b != '#' else b for (a,b) in zip( tetromino[i], field[r+i] ) )
# check for completely filled rows
if field[r+i] == '#' * 10:
# remove current row
del field[r+i]
# add new row
field[0:0] = [' '*10]
field[7] += 10
# we found the row, so abort here
break
# print it in the requested format
print( '\n'.join( '[' + r + ']' for r in field[:7] ) )
# and add the points = 10 * the number of redundant lines at the end
print( str( field[7] ) )
