31
I'm sure there are more than 2 prime numbers that are 400 digits long.
The number is 84.
There is no specific name: you just call it a number with 2 or more digits or a multi-digit number.
50
We generally refer to them by the number of digits. Two-digit number, three-digit number, etc.
A quintillion is a number with 18 zeros (19 digits). A 20-digit number would be 10's of a quintillion (20 digits since we add one more digit to the left).
17
Every square of a 4 digit number has more than four digits.
The odd prime digits are 3, 5, and 7. but the final digit of your three-digit prime number can't be 5. So there are only 18 combinations to check. You can list these numbers and start going through them to see which are prime. The easiest test is divisibility by 3 (sum the digits) and that quickly eliminates 7 of them. You are left with:337353373533553x557577733737x757773Of these, only two are not prime. I marked them with an "x". I used a table of primes to find these and don't know an easier way.
2.3
The question cannot be answered. All that I know about your number is that is has at least 4 digits. Your number could be a hundred digits long - I have no way of knowing.
There are an infinite number of prime numbers beyond any fixed number of digit you could ask about. Even if we had all the computer power to find such a number what makes you think I am going to write a million digit answer. And even if I did how would you know it was right. It is not like you are going to do anything useful with this knowledge.