How we will come to know whether its for FDD or ZDD? In general, one has to say so, but there are certain edges that can only occur in BDDs or in FDD/ZDDs. You cannot distinguish FDDs and ZDDs from each other (since their graphs look the same, but encode different boolean functions as either FDD or ZDD in general).

To get a RMNF, it is best to first derive the boolean function in a full DNF. Looking at your BDD, the function is c&!b | !c&a. Now, a full DNF would be

!a&!b&c | a&!b&c | a&!b&!c | a&b&!c

These are all satisfying assignments (without don't cares). The RMNF is now obtained by replacing the disjunction with xor operations and the negations by xor with true:

(a⊕1)&(b⊕1)&c ⊕ a&(b⊕1)&c ⊕ a&(b⊕1)&(c⊕1) ⊕ a&b&(c⊕1)

Now, we have to apply distributive laws (and note that x⊕x=0):

a&(b⊕1)&c ⊕ (b⊕1)&c ⊕ a&(b⊕1)&c ⊕ a&(b⊕1)&(c⊕1) ⊕ a&b&(c⊕1)
= (b⊕1)&c ⊕ a&(b⊕1)&(c⊕1) ⊕ a&b&(c⊕1)
= b&c ⊕ c ⊕ a&(b⊕1)&(c⊕1) ⊕ a&b&(c⊕1)
= b&c ⊕ c ⊕ a&b&(c⊕1) ⊕ a&(c⊕1) ⊕ a&b&(c⊕1)
= b&c ⊕ c ⊕ a&(c⊕1)
= b&c ⊕ c ⊕ a&c ⊕ a