A "second home" is a secondary residence which you do not primarily live in, so will you be living in this new home a majority of the time? If so, then it will be your primary residence.
Unless your sister refinances before your new purchase is completed, that won't be factored in if you are doing Fannie or Freddie financing on the new purchase.
Yes, gift funds can be used as reserves, see https://www.fanniemae.com/content/guide/selling/b3/4.3/04.html (although lenders may have overlay guidelines that prevent then being used as reserves, which I've seen before).
Free Mortgage Advice & Pre-Approvals (FHA, VA, USDA, Fannie, Freddie, Non-Prime, Construction, Renovation/Rehab, Commercial) since 2002
Located in Southern California and lending in all 50 states
It's been 14 years since I've stepped into a new home.... refinanced this year, but it was FHA, so it's all new ... and kinda confusing!! Appreciate the guidance