Is it necessary to renew the marriage if it was invalid and the wife became Muslim, and is it permissible to appoint a Muslim as her guardian, or must her mother be informed?

Your marriage is invalid because it took place without the presence or authorization of the woman's guardian (wali). The most rightful guardian for your Muslim wife is her Muslim guardian, in order of precedence. Her disbelieving guardian cannot give her in marriage, by consensus of the scholars. If there is no Muslim guardian for her, then a Muslim judge should give her in marriage. If there is no such judge, then a just Muslim man should give her in marriage. You are not obligated to inform her mother, although informing her is among noble character traits.