It took me a while, to actually understand the question.
To your first question:
No, this kind of scheme has no name, because it is actually worse than any of the classical ciphers. Well, if you consider any substitution table (over 26 letters) a variant of the Caesar cipher, then... you have such a variant. But it is much weaker than the random substitution, and probably even weaker than the original Caesar cipher. As far as I know, this has no name, and it is surely not a classical cipher. The weakness is really obvious: The later part of the alphabet is just the identity, and this is known even before looking at frequency analysis.
Considering your "improvement", this is not a Vigenere variant, because you actually have a static shift of the substitution by 1 letter each step. So your period is static (26), and you don't gain much of an advantage.
Considering your last "variants"... I have no idea what you actually try to achieve. Leaving out spaces or "ordering them in blocks with fixed size" is not gonna matter. This is no security measure. You are not adding "complexity", you make it more complex to use the cipher for no reason.