I think I have an idea how to truly generate true random, non-deterministic numbers.
If you have a normal computer you actually can't create truly random numbers, unless you have dedicated hardware (hardware random number generator) that produces truly random numbers. If you don't have that then the best you can do are Cryptographically secure pseudorandom numbers.
What kind of numbers are needed for cryptography/security? Are those integers?
Once you have a random number you can also change the representation of it, for example an interger, Hex, binary, etc. It depends on the usage.
- Do you need a salt? $\rightarrow$ alphanumerical
- Do you need it for mathematical cryptography like asymmetric encryption? $\rightarrow$ integer
How long should those numbers be? 10 digits, 100 digits?
The encryption scheme known as RSA uses fairly large prime numbers i.e. 1024-bit ($\approx$ 310 digits). You generate a 1024-bit number and increment the number until you have reached a prime number. This answer gives some additional information.
If you want to create a simple coin-toss application you only need to produce a 1-bit random value (i.e. $0 =$ head, $1 =$ tails).
[$\ldots$] did I get it right, random numbers are used to create hashes to create stronger encryption?
Random numbers have a large application (especially in cryptography).
Hashes are deterministic. That means that some input always has exactly the same hash-value. No matter when, where or anything, an identical hashing-algorithm creates always the same hash-value for an identical input. The idea of random numbers is that they create (almost every time) a different number.
Random numbers indeed play an important role for encryption. Almost every encryption-scheme makes use of random number generators.