Is the following scenario correct about federal filing status?

a)$)$ An unmarried taxpayer has earned income of $96$\mathrm{}\mathrm{}$K.$.$ The taxpayers single mother does not live with the taxpayer and has no income, so the taxpayer provides 100%$\mathrm{}\mathrm{}\mathrm{}$ of the mothers support. The taxpayer can file as HOH

b)$)$ A dependent child has started an odd jobs service over the summer and has earned $1625$\mathrm{}\mathrm{}\mathrm{}\mathrm{}$ from multiple customers. The dependent can file as Single

c)$)$ A taxpayer and spouse who are in a registered domestic partnership can file as MFJ on their federal return

d)$)$ An unmarried taxpayer has a child born in Dec of the current tax year. The taxpayer has an earned income of $19500$\mathrm{}\mathrm{}\mathrm{}\mathrm{}\mathrm{}.$ The taxpayer can file as Single

e)$)$ A taxpayers divorce is not finalized on the last day of the tax year, but they are legally separated. The taxpayer can file as Single