I understand that Texas was an independent country for some period of
 its history.
 I would be delighted to know the following:
 - Which specific years it was independent?
 - Who its leaders were during this period?
 - What other countries it had exchaged ambassadors?
 - What was its capital?
 
  Cheers

  Mongolia

Hello mongolia~

On March 2, 1836, The Texas Declaration of Independence was signed and
a temporary government was formed:

* David G. Burnet, President  (see Lone Star Junction:
http://www.lsjunction.com/people/burnet.htm )

* Lorenzo de Zavala, Vice-president (see Handbook of Texas Online:
http://www.tsha.utexas.edu/handbook/online/articles/view/ZZ/fza5.html
)

* Samuel P. Carson, Secretary of State

* Thomas J. Rusk, Secretary of War (see Lone Star Junction:
http://www.lsjunction.com/people/rusk.htm )

* Bailey Hardeman, Secretary of Treasury (see Lone Star Junction:
http://www.lsjunction.com/people/hardemwp.htm )

* David Thomas, Attorney General

To see the Declaration, go to Lone Star Junction, ?The Texas
Declaration of Independence? : http://www.lsjunction.com/docs/tdoi.htm

The committee creating the Declaration was: George C. Childress (see
Red River Authority:
http://www.rra.dst.tx.us/c_t/people/gcCHILDRESS.cfm ), Edward Conrad,
James Gaines (see Handbook of Texas Online:
http://www.tsha.utexas.edu/handbook/online/articles/view/GG/fga4.html
),  Bailey Hardeman, and Collin McKinney.

The First Texas Congress assembled on October 3, 1836. On October 22,
the Republic of Texas named General "The Raven" Sam Houston its
president and Mirabeau B. Lamar (see Texas State Library:
http://www.tsl.state.tx.us/treasures/giants/lamar/lamar-01.html  ) its
vice president. (Mirabeau B. Lamar was also the Republic?s second
President.) Houston named Stephen F. Austin  (see PBS:
http://www.pbs.org/weta/thewest/people/a_c/austin.htm  ) was named
secretary of state; Henry Smith, secretary of the treasury; Thomas J.
Rusk secretary of war; Samuel Rhoads Fisher secretary of the navy; and
James Pinckney Henderson, attorney general.

Congress chose Houston as the temporary capital, and in April of 1837,
the government moved there. In January of 1837 the permanent capital
was chosen and named: Austin.  In October, the government moved to
that location.

On December 29, 1845 Texas became a state.

It is doubtful that any countries formally exchanged ambassadors with
the Republic of Texas; it was a fledging little place, constantly
fighting to keep Mexico at bay and struggling financially.

For an in-depth look at the Republic of Texas, check out ?Republic of
Texas,? The Handbook of Texas Online:
http://www.tsha.utexas.edu/handbook/online/articles/view/RR/mzr2.html

Regards,
Kriswrite

KEYWORDS USED: 
Republic of Texas
://www.google.com/search?hl=en&lr=&ie=ISO-8859-1&oe=ISO-8859-1&q=Republic+of+Texas

Individual searches for each name mentioned above

Thanks for some very interesting information. 
 Mongolia

Mongolia, thank you for the terrific rating and the tip! I appreciate both :)

Kriswrite

Texas had an ambassador from France set up east of downtown. I was
there a few weeks ago, it?s called the French Legation.

http://www.frenchlegationmuseum.org/

Texas was recognized as a country by several other countries
(including the US, France, England and the Netherlands) and I'm pretty
sure had at least a couple of embassies. I've seen the buildings that
supposedly housed the London and Paris embassies.