<image> Observe the diagram and solve the following questions.
(1) The small circles in the diagram are divided into six layers by broken lines. The first layer has 1 small circle, the second layer has 3 circles, the third layer has 5 circles, ..., the sixth layer has 11 circles. If you were to continue drawing, how many small circles would there be in the eighth layer? And in the nth layer?
(2) If a certain layer has 65 circles, which layer is it?
(3) There are several different ways to count the number of circles in the diagram. 
For example, the sum of the circles in the first two layers is (1+3) or \(2^2\), 
thus, 1+3=2^2. Similarly,
the sum of the circles in the first three layers is: 1+3+5=3^2.
the sum of the circles in the first four layers is: 1+3+5+7=4^2.
the sum of the circles in the first five layers is: 1+3+5+7+9=5^2.
...
Based on the above, can you conjecture what the sum of the first n consecutive odd numbers is? Express it using a formula.
(4) Calculate the sum: 1+3+5+...+99;
(5) Calculate the sum: 101+103+105+...+199.