>>4
No. Just because a sequence is uncomputable in general doesn't mean a specific term in the sequence cannot be computed.
>>6
A function
g\colon\mathbb{N}\to\mathbb{N} grows faster than all computable functions if every computable function
f\colon\mathbb{N}\to\mathbb{N} satisfies
f(n)<g(n) for all sufficiently large
n.