help regarding binomial heap and fibonocci heap

hi all
I am rupesh kumar form India and currently i am a M.C.A student of Pune university .i want one favour from your side if possible plz help me .i have some question regarding Binomial heap and fibonacci heap and i wantanswer of these question ,Questions are.

1-:What is the impact of calling Merge from Insert/Union on the amortizedcosts ?

2-:Why allow atmost one child to be deleted ? What happens if we allow 2,3,... m children to be deleted. How long can we guarantee O(c^k) nodes fora Uk tree ?

3-:How do we "physically" relate fibonacci numbers with the fibonacci heap? Which operations intuitively tell us that its related to fibonacci number?

4-:To prove that with first two modifications, 1) min ptr 2) allowing more than one tree of a given degree, the maximum degree of a tree is O (lg n).

5-:Is it possible to improve upon binomial heap, without "delaying" themerge or push-up of smaller-key nodes ( or without trying
amortized-design) ?

6-:Binomial trees can be corelated with binary number system. Which number system can fibonacci heaps be corelated with? how?

i will be very grateful if you tell me the answers of these question
with explanation its very urgent. and you can post the answer in my mail id
rupeshdwivedi007@gmail.com
or
u03127@cs.unipune.ernet.in

thanks in advance

RUPESH KUMAR