Hi OP, my son started with a childminder at 15 months, and I remember the process of finding one all too well! I must have spoken to at least 20 before deciding on our current childminder, who is wonderful. I hope you can find the equivalent person for your little one!
In terms of qualifications etc, I asked childminders to send over their policies and documents for me to review (they have to have them all ready to view in order to maintain their Ofsted registration), and we also met up several times before DS started with her. I was happy with what was sent, as well as the Ofsted inspection reports. She in turn asked us for lots of information about DS, his development and routines, any challenges, photos of family/pets, favourite books etc. She suggested that we start to introduce certain things in advance of him starting to make the transition smoother (eg more independent drinking from a bottle, not just an open cup) which I really appreciated.
In terms of the childminder having her own son, this would not concern me at all personally, and from memory he will have been declared to Ofsted as a person present in the house (a qualified CM poster might be able to confirm this, apologies if I’m wrong) although if he’s under 16 he won’t have been DBS-checked. You could ask to meet him just to say hello/as part of viewing the setting. Same with any husband/partner she may have. I think it’s ok to want to meet people who will regularly be around your children.
In terms of other tips, I think it depends what you are looking for from a childminder. I wanted to know which groups she went to, examples of multi-age activities (ours has 3 children incl. DS of differing ages), how naps worked, any equipment I would be expected to provide, breastmilk storage protocol, how trips out and about worked practically with multiple kids (this makes me laugh looking back, but I’m glad I asked anyway), what books she had… You’re paying for a more bespoke service than a nursery and that has huge advantages in my view. There are also downsides, such as reduced flexibility. So asking about illness/holiday policy is sensible. If she can tell you her holidays up front, you are in a better position to book leave from work etc.
Best of luck to you!