These all work in both present and past tenses.
(While you're at the concert, listening) - I'm glad you like the music. (After the concert, when you're remembering) - I'm glad you liked the music.
Your last line is a bit twisted. (past tense) - "I'm glad that you were happy with my work." (present tense) - "I'm glad that you're happy with my work."
"I'm glad that you happy with my work" is ungrammatical. The "that' clause has no verb.
Best wishes, - A