1.  1810 Census:  "James Thompson," head-of-household, Christian Co., KY.  See Table.  There are two.

2.  Cordelia C. Gary.  1970.  Marriage Records, 1797-1850, Christian County, Kentucky.  LDS Film No. 0496899.  List of marriages for those requiring parental permission (i.e., underage marriages).  A James THOMPSON gave permission for an underage Sarah to marry; he is most likely Sarah's father, but could be an uncle or older brother, etc.

THOMPSON, Sarah to Simon KUYKENDALL, 28 July 1802, James THOMPSON

3.  From The Kentucky Land Grants by Willard Rouse Jillson (1925, Filson Club Publ., Louisville, KY; reprinted 1994 by Genealogical Publ. Co., Baltimore, MD; also online at Ancestry.com).  C = Christian Co.;  H = Hopkins Co.; T = then Logan Co., but now Todd Co.  The number is the number of acres.  An examination of the county deed books for the sale of these lands could determine which James Thompson owned which parcel.  (And could "N." be a misreading of "M."?):

Northern Christian Co./Hopkins Co. land grants:

Thompson, James, Sr.	120	15 Feb 1799	West Fork Pond River	C
Thompson, James	100	18 Apr 1803	Pond River	C
Thompson, James	100	11 Apr 1803	Tradewater	C
Thompson, James N.	45	3 Jan 1807	Tradewater	C
Thompson, James N.	200	2 Jan 1807	Barren Fk, Tradewater	C
Thompson, James M.	100	7 Sep 1810	Tradewater	C
Thompson, James	500	13 Feb 1822	Trade Water River	H

The W Fork of the Pond R. runs from north-central Christian Co. northeastwards to join the Pond R. as the boundary between Hopkins and Muhlenberg Cos.
The Tradewater R. runs from north-central Christian Co. northwestwards to become the boundary between Hopkins and Caldwell Cos.  I have yet to locate the Barren Fork of the Tradewater.

Central/southern Christian Co. land grant:

Thompson, James

150

31 Mar 1817

Little River

C

The North Fork of the Little River runs westward through Hopkinsville.  The South Fork runs westward south of Hopkinsville — both into what is now Trigg Co.

Todd Co. land grant:

Thompson, James

400

29 Sep 1803

Elk Fork, Red River

T

The Elk Fork of the Red R. runs from central Todd Co. [at the time, Logan Co.] southeastwards into Tennessee.

4.  Southern Christian County, KY, Cemetery Records. LDS Microfiche #6075676.  In the Johnson Mill Road Cemetery, near Hopkinsville, Christian Co., KY:

p. 293

James Thompson

b. 1802

d. 6 July 1864, age 62y

This record may apply to the James Thompson who is husband of Elizabeth [West?].