Visa for child born in the UK

Hi All,

Hope everyone if okay.

Could I please ask for some help on the following questions? These are with regards to my child's visa born in the UK.

a. How many months(or years) would a child born(not UK citizen) in the UK be allowed to have no visa, in the basis that they are new born? If you have a link of this rule on the UKBA site, please include them for my own reference in the future.
b. Do I need to get a copy of the sponsor's registration details for applying for my child's visa? Please specify all that I need or should I just need my own and partners visa details?
c. My partner is changing her name on her passport, would there be any cost in changing her name to her visa? Could I just include this with my child's visa application?
d. How do I sign for my child's application, should we use her thumb print? And does a baby required to take bio-metrics on UKBA or the post office?
e. Would there be any restrictions for us getting child tax credits since we are on Tier 2 which specifically says that "no recourse to public funds"? And how would you identify which is which? As far as I remember, if you apply for ILR, the applicant may get charged for getting any form of benefit.
f. Are there any form of child credits that we could use that would not affect any future applications of visas and the ILR?

I would really appreciate if anyone would be able to give us some answers to these questions and links as reference. I'm been looking at the UKBA site and could not find the documents which are related to these questions.

Kind Regards,

Jin

a. Indefinitely.