"I like the lamp."
Translation:Ich mag die Lampe.
Grammar is fine. Normally, we use 'gern haben' more for people or animals than for objects. So, it sounds a bit strange to say 'Ich habe die Lampe gern'.
That doesn't make much sense. You probably meant "Ich hätte gerne einen Termin" which translates to "I would like to make an appointment"
"Die Lampe" is feminine, and in this sentence the lamp has taken the accusative (you can think of it another way as being "The lamp is liked by me") -- the feminine article does not change with the accusative case. See this page for a good resource on the different cases and the article transformations: http://german.about.com/library/blcase_sum.htm.
Please don't use the discussion area for error reports or to suggest alternative translations. Better use the in-lesson report function. That way, the right people will receive your message. Thanks!
Is there anything wrong with "Ich die lampe gern"?