$\alpha-D-(+)$-glucose and $\beta-D-(+)$-glucose are

What is the number of primary and secondary alcoholic groups respectively present in glucose?

Statement $I$. Despite having an aldehyde group,glucose does not give the Schiff test.
Statement $II$. Glucose exists in $\alpha$ and $\beta$ crystalline forms.

Compound $A$,$C_5H_{10}O_5$,gives a tetraacetate with $Ac_2O$ and oxidation of $A$ with $Br_2-H_2O$ gives an acid,$C_5H_{10}O_6$. Reduction of $A$ with $HI$ gives isopentane. The possible structure of $A$ is:

$CHO-(CHOH)_4-CH_2OH \xrightarrow{HIO_4} \text{Product}$. Identify the product.

The standard compound for determination of configuration in the 'sugar chemistry' is