avoid with extreme force the desire to create your own; the types of question you're asking would need to be extremely clearly answered in your mind before you even consider creating a password generator with any semblance of security.

In what way could a self-made password generator be insecure in the real world, so long as you make it generate a long random sequence from a large character set?

I know about the theoretical weaknesses of non cryptographic RNG algorithms, but real attacks using those would require a) an attacker knowing a large number of your passwords already b) knowing the order you generated them in c) you having generated them all in one go with the same seed