Will checking my score on Fold reduce it? / Is this a "hard pull" or a "soft pull"?

No, checking your score on Fold will never lower it. Fetching your own report is treated as a "soft inquiry." 

Soft inquiries have zero impact on your score, regardless of how often you check. A score only drops from a "hard inquiry," which happens when a bank or lender checks your profile because you officially applied for new loan or credit card.