Human beings have their own ways to express their feelings of grief and sadness as well to express their feelings of happiness. Islam allows different ways of expression of feelings as far as it does not contradict a clear ruling of Islam. No one can express his happiness by dancing, simply because dancing is forbidden in Islam. No one can express his sadness by drinking beer or alcohol, simply because drinking alcohol or beer is forbidden in Islam.
People whom you mentioned in your question are expressing their feelings of grief by their own way which does not contradict with any Islamic clear rule, and does not have bad effect on the image of Islam.
Allah (SWT) grants people the reward according to their intentions. These people are observing and remembering the tragedy of Karbala. May Allah (SWT) grant them reward according to their intentions.
Repeating Isteghfaar (Seeking forgiveness) is very helpful for every one especially those who feel guilty.
Remembering Allah and taking His names and repeating it is very useful in treating depression or anxiety or any psychological problem. Remembering Allah keeps the heart peaceful and prevents the causes of depression. More remembering Allah (SWT) brings more peace and comfort in the heart and mind.
I am truly sorry to hear of the loss of your mother. Our condolences.
There is a difference between grief and longing. You will always long for her presence, especially on days of importance, days of sorrow and days of hardship, but grief is temporary. You must accept grief as a part of the healing process, and you must accept the position that you are in.
Loosing your mother might have pushed you into a dark hole, and instead of struggling to get out, you must let go and let yourself fall into the darkness of it. Only when you reach the bottom you will be able to rest. Holding on to the wall of the hole, you use all your strength to reach the top, but what if you aren’t supposed to reach the top yet? If you let go and find a way to accept your position, meaning your position of sorrow, then you can gain strength to climb out of the hole. Accept that it hurts, and accept that every hardship, every sorrow, and every grief are different. We react differently, and we must give ourselves time to heal. It is your loss and you are the only one entitled to control the grieving process.
Everything in life is part of a perfect system. After the darkness of winter, the spring blossoms. After the darkness of the night, the sun rises. After every hardship there will be ease. Death is a part of that system, and sorrow too. Do not fight the pain, welcome it and let it hurt because nothing hurts forever. One day you will awake and the sun will shine a bit brighter, the ray of sunshine will be a bit warmer, and the beauty of spring will blossom again. Before that, you must rest at the bottom of the hole in what seems like complete darkness. Only after true darkness we appreciate light, but in reality, nothing is ever completely dark. It takes a lot of darkness to cover the light, but it takes a small part of light to change the dark.
You will get through it, though it might not seem like it right now. Allow yourself to feel the pain and allow yourself to grieve in whatever way you need to. Imam al-Sadiq (a.s.) said, ‘Verily when someone dies, Allah sends an angel to the most grieved member of his family, who strokes his heart and makes him forget the agony of grief, and if it were not for this, the world would never again thrive.’[al-Kafi, v. 3, p. 227, no. 1]