There are two varieties, one with a normal date and one with a recut date. Numismedia lists the following approximate retail values as of 03/2010:
Normal date:
Very worn condition - $17
Moderately worn - $28
Slightly worn - $37
Almost no wear - $103
Uncirculated - $138 to $1,040 depending on quality
Recut date:
Very worn condition - $150
Moderately worn - $330
Slightly worn - $432
Almost no wear - $895
About 1 cent.
35.00
Sorry no US 2 cent coins dated 1863
About a dollar depending on its condition.
The coin's still in circulation and is only face value.
Please check your coin again and post a new, separate question. The US never minted a 2.5 cent coin.
A 1997 US one cent piece? is a Lincoln cent and only face value.
About 1 cent.
35.00
Sorry no US 2 cent coins dated 1863
A "dime", or ten-cent piece, has a value of 0.1 dollars.
About a dollar depending on its condition.
No gold US one cent coins were ever made.
Sorry no US 20 cent coins dated 1802
The coin's still in circulation and is only face value.
No such (US) coin exists because the copper-nickel 3 cent piece was not minted until 1865.
A US steel Lincoln cent is 5 to 10 cents in average condition.