QDoes hSD01-006〈Tokino Sora〉's Arts 'SorAZ Sympathy' get 'Arts +50.' even when hSD01-013〈SorAZ〉 is among your holomem?

AYes, +50 will be added.
Even if there is no corresponding card name, if there exists a card with an extra like 'This holomem is also regarded as 〈Tokino Sora〉〈AZKi〉' as specific card names, the condition is met.

QFor hSD01-006〈Tokino Sora〉's Arts 'SorAZ Sympathy', does the condition 'If an holomem is on your stage' still apply if hSD01-013〈SorAZ〉 is present?

AYes, it meets the condition.
Even if there is no corresponding card name, since it is written in the Extra that 'This holomem is also regarded as 〈Tokino Sora〉〈AZKi〉', the condition is met.