A dead heart

I was walking at the bay
Listening to the whisper of sea
Feeling the warm breeze
While waiting for the sunset

^^
First line: Personally, I have an issue with 'at' - I don't know why, just to me it sounds wrong somehow. Yet, it makes sense, so I don't know. Ignore me.
Second line: Reading this line makes me picture a person holding a sea-shell to their ear -- I don't know why that would be when that person is clearly stated to be already on the beach.. but that's the image in my head. lol
Third line: This line - well the whole stanza really - it brings on feelings of passion and love, but considering this is in the 'sadness and depression' folder I don't think this is the case, at least not anymore.
Fourth line: 'sunsets' the ultimate love-fest symbol (besides the loveheart of course)

I was standing alone
Still hoping he would come
Thinking of the past time
When he was all, fully mine

^^
First line: There's the sadness! It's never nice to be stood up, especially in a setting as romantic as you have described. It makes that person feel unworthy and unloved when in reality it's more likely the wrong person - your soulmate has just not found you yet.
Second line: Oh, and to still have the 'hope' - that would just make the outcome even more difficult to bear.
Third line: I love that you added this line - it's so simple but it gives you an action while you're waiting... reminiscing
Fourth line: Personally, I don't like this line - I think it is the 'fully mine' at the end - it just sounds too immature for the poem which actually has some maturity about it, so it doesn't really fit. Perhaps try 'entirely' or 'completely' ?? Other wise, the line is okay.

This sunset are the memories
Of those sweet and tender kisses
Of those warmth and tight hugs
When we're spending for the cold nights

^^
First line: 'are' doesn't sound right though (I think) I understand what you're trying to say. Perhaps try: 'This sunset is filled with memories.. ?? OR 'These sunsets are the memories'...? I don't know. The line just needs a little work.
Second line: This line is perfect - innocence and passion - a beautiful mix that is often difficult to achieve.
Third line: Alteration needed. Either 'that warmth' or 'those warm' -- your pick.
Fourth line: To me this line doesn't make sense. I think it is the word 'spending' - I think you're trying to stay your giving each other these hugs and warmth on the cold nights - It may also be the 'when' at the beginning -- I'm not sure. This line needs revising.

And now those time fade
My heart seems now dead
How he left my heart breaks
And now it still aches

^^
First line: 'time' should have an 's' on the end OR 'those' should become 'that' with an 's' also on fades. Again, your choice.
Second line: Instead of 'seems now dead' change to 'now seems dead' - more grammatically correct. This is a powerful line; it shows the extent of your emotions.
Third line: Revise this line. Either: 'How he has left, my heart breaks' OR How he left, my heart is broken' OR 'Now he left, my heart breaks' (the least amount of change, but it does change the current meaning) - Or something similar to either of those.
Fourth line: The continuity of the emotion.. I like how you left this open - readers have no knowledge of how long it has been - it could have been today, yesterday, a year ago - we don't know, and it makes us think.

I am here walking, walking alone
For those moments are gone, and no time for fun
I am here crying, crying for pain
For he breaks my heart, a heart that's now dead...

^^
First line: Great repetition - it's used well. Good imagery too.
Second line: Personally, I don't think the 'no time for fun' is necessary in this line. But either way, end this line in a fullstop.
Third line: A powerful line; the imagery is beautiful, and the sorrow is clearly stated. Expressed perfectly.
Fourth line: Again, the extent of that emotion - the sorrow, the pain - the effect that it has had on you.

Overall;
A really fantastic piece!!
I know I critiqued it throughout - maybe too much, but.... these are ultimately to help you improve the piece. I hope I have been of help, if not, completely ignore me.
Sometimes I ramble - sorry! - but I think I got to the point in the end.
Your expression was definitely your strong point here - don't let that fade, because it is such a powerful gift, especially in poetry.

Your ending was very powerful - and it really let those emotions shine through, kind of a peak of the piece. Brilliant.

Well penned. 5/5

I'm here crying, crying for pain
For he breaks my heart, a heart that's now dead....
What a powerful line. 5/5