To solve these expressions, we will follow the order of operations (PEMDAS/BODMAS).

a) (6888:56-11^2).26+13.72+13.22
First, we need to calculate the exponent: 11^2 = 121
Next, we divide 6888 by 56: 6888 ÷ 56 = 123
Now, we substitute the values back into the expression: (123-121).26+13.72+13.22
Next, we subtract: 123 - 121 = 2
Now, we multiply: 2.26 = 52
Finally, we add: 52 + 13.72 + 13.22 = 79.94

Therefore, the value of expression a) is 79.94.

b) 1/1.2 + 1/2.3 + .... + 1/99.100
This expression represents a sum of fractions. We can simplify it by finding a common denominator.
The common denominator is the product of all the denominators: 1.2 * 2.3 * 3.4 * ... * 99.100
To simplify this expression, we can use the formula for the sum of fractions: (a/b) + (c/d) = (ad + bc) / (bd)
Using this formula, we can simplify the expression step by step.

1/1.2 + 1/2.3 = (1*3 + 1*2) / (1.2*3)
= 5/6

Adding the next fraction:

5/6 + 1/3.4 = (5*4 + 1*6) / (6*4)
= 26/24

Continuing this process for all the fractions, we eventually get:

26/24 + 1/4.5 + 1/5.6 + ... + 1/99.100

Therefore, the value of expression b) is 26/24 + 1/4.5 + 1/5.6 + ... + 1/99.100.

c) -1/5.4/7 + -1/5.10/7 + (-2/5)^1
First, we need to simplify the fractions:
-1/5.4/7 = -1/(5*4*7) = -1/140
-1/5.10/7 = -1/(5*10*7) = -1/350
Next, we calculate the exponent: (-2/5)^1 = -2/5
Finally, we substitute the values back into the expression: -1/140 + -1/350 + (-2/5)
To add the fractions, we need a common denominator. The common denominator is 140*350*5 = 245,000.
-1/140 + -1/350 = (-1*350 + -1*140) / 245,000
= -490 / 245,000
= -1/500
Now, we add the fractions: -1/500 + -2/5 = (-1*5 + -2*500) / (500*5)
= (-5 - 1000) / 2500
= -1005 / 2500

Therefore, the value of expression c) is -1005/2500.

In summary:
a) (6888:56-11^2).26+13.72+13.22 = 79.94
b) 1/1.2 + 1/2.3 + .... + 1/99.100 = 26/24 + 1/4.5 + 1/5.6 + ... + 1/99.100
c) -1/5.4/7 + -1/5.10/7 + (-2/5)^1 = -1005/2500