Does xbox live gold membership stack when I purchase a new one?

Yes, they do. You can lock the lower price so when it auto-renews you save $20.

See here

One year subscription at $39.99 for the first year with auto-renewal at the then current annual price following year one

Yes, additional purchased membership time will stack. In addition to the one-year lock-in price currently offered by Microsoft, you can buy scratch cards at pretty much any retailer where games are sold. These can be bought at the current subscription price, and redeemed either now (and stacked with existing time) or sold to your friends later for a teeny tiny profit.