No.
Although the ratios of the terms in the Fibonacci sequence do approach a constant, phi, in order for the Fibonacci sequence to be a geometric sequence the ratio of ALL of the terms has to be a constant, not just approaching one.
A simple counterexample to show that this is not true is to notice that 1/1 is not equal to 2/1, nor is 3/2, 5/3, 8/5...
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The 20th Fibonacci number in the sequence is 6,765.
The Fibonacci sequence requires two numbers as "seeds".
42
No, the Fibonacci sequence never ends. It just keeps on going!
A few examples: Counting numbers are an arithmetic sequence. Radioactive decay, (uncontrolled) bacterial growth follow geometric sequences. The Fibonacci sequence is widespread in nature.