Yes it is grammatically correct, but I agree with annettepicconi, we would generally describe the clothes as 'warm' rather than 'heavy' in this context. However as she says in her example; when winter is over you can express relief at no longer having to wear 'heavy clothes'

It depends on the context and who's saying it. As Miller says, it can (mainly in American English) mean to do something very well. Usually said by younger people and with some excitement e.g. "He handled that car like a boss!" Otherwise, if used in a more serious way, I'd agree with Richard's explanation that it describes someone who is acting in a controlling or demanding manner. We also use "bossy" or "boss about" in this context too: "She's a very bossy person!" "Stop bossing me about" Best wishes :)

Depending on the trouble, I think this really is a case where your tone and manner means more than the words you say. Just listening and making sympathetic noises is usually a good start :) One of the best ways to comfort someone is to try to show them that you understand the difficulty/pain/whatever they are experiencing rather than trying to make it better or tell them it's going to be ok. So some useful phrases might be: "It sounds like things are really tough for you right now" "That must be really painful/difficult" "I'm sorry that xxxx happened to you" If it's someone in real distress and just needs some comforting words like a little child, then we generally say things like "There there", "It's ok" "You'll be ok" "You'll be alright" It is difficult to know the right thing to say to someone even in your own language so I would not worry too much. Just saying something gentle and genuine will be appreciated even if the English is not perfect!