As the other posted stated, it would be better to describe your problem before the statements. Also, "We would appreciate if you would instruct the garbage collectors" sounds more natural than "We would appreciate it if you give appropriate instructions to the garbage collectors" One more thing - are you speaking to a US or UK audience? "Rubbish" works great for British speakers but would be odd in the US ("trash" is far more frequently used here).

It makes sense, but you might want to put at the beginning of the letter your problem: that your waste is not being collected promptly. After that I would insert what you said. Stating your problem first provides some context to what you are saying.

You wouldn't typically "give instructions" to someone to be prompt. You might "remind them of the importance of being prompt" for example.