the girl married a Muslim guy and then adopted a Muslim name and converted to Islam as is the norm. now they got divorced in 2013. the girl is technically a Muslim as she converted to Islam when she got married. therefore if you wish to marry her, you can do so but only under the SMA.
if she reconverts to Hindu (Sikh) then you can perform Arya samaj marriage followed by a registered marriage.
the divorce took place in 2013 when triple talaq was still legal in India, therefore, it is the intention of the parties which alone matters and in this case the parties have wilfully stated that.
the first marriage of the girl was not under the special marriage, it was a nikaah as she converted to Islam.
yes, the document is sufficient as there are 2 witnesses too.
the present status of the girl is of a divorcee, she is a Muslim. you should not apply for a visa as single and unmarried.