"about four years ago."

The Ownership provision and the Use provision are separately evaluated.

Gross income shall not include gain from the sale or exchange of property if, during the 5-year period ending on the date of the sale or exchange, such property has been owned and used by the taxpayer as the taxpayer’s principal residence for periods aggregating 2 years or more.

"How do they determine the basis of the 10 acres of land sold?"

10/15. They sold 2/3 of the land.

"Not sure if the original appraisal breaks out the home and land value."

Did you look at the tax records? If nothing else, it should show the different property types (land, improvements) and that gives you the ratio of what they paid, for purposes of acreage vs residence on its parcel.

"I've read that in some cases one can use the property tax evaluation."

If it's anything like MT, the valuation isn't what they paid. You don't need what is was "worth" for tax purposes. Basis + improvements including filing for variances and/or survey, deed/title issues.

"Also, the two sales were to two different parties, would the $500,000 gain exclusion apply to both sales?"

(3) Vacant land—(i) In general. The sale or exchange of vacant land is not a sale or exchange of the taxpayer's principal residence unless—

(A) The vacant land is adjacent to land containing the dwelling unit of the taxpayer's principal residence;

(B) The taxpayer owned and used the vacant land as part of the taxpayer's principal residence;

(C) The taxpayer sells or exchanges the dwelling unit in a sale or exchange that meets the requirements of section 121 within 2 years before or 2 years after the date of the sale or exchange of the vacant land; and...

You're going to need to learn how to use IRS and web resources. Try this link:

https://www.law.cornell.edu/cfr/text/26/1.121-1

Intuit isn't giving you access to ProConnect for free? Sheesh.