著急-Be afraid of running out of time. 担心 - Be worried about 时髦-Posh 70% fashion 30% . 流行 - Trendy , Up to date. 了解-Understand (Without thinking) 理解- Realize.(By using brain) 熟练-Things that you always do and now it's easy for you(taking bus,making sandwich...etc) 擅长 - Skill at (Cooking,swimming...etc)

hello.Maybe I can help you. 着急:do sth. in a hurry. eg.我急着去赶公交车。or 我很着急。 担心:be worried about sth./to do sth. eg. 我担心的事还是发生了。 or 我担心ta的身体。 时髦:sth.very 时髦 eg.你的发型很时髦。 流行:styles very 流行 or someting is very popular. eg.这种风格现在很流行。 or 现在流行这些东西。 p.s The two words in chinese meaning actually. 了解:know about sth. 理解:understand (Generally refers to understand knowledge,words such as deeper meaning.) 熟练:do sth. very 熟练。 eg.我骑自行车很熟练。 擅长:be good at.. 擅长+do sth..eg. 我擅长画画。 I'm not good at English .I hope you could understand what I say.（＃￣▽￣＃)

There are four groups synonyms in your question. As a native speaker, this is my understanding below: 1. 着急 which describe that people wish get a better( or quicker) progress about something or somebody even a result. eg. 我很着急我的汉语学习。（我对我的汉语学习很着急）。 担心 means worry about... eg.我担心我不能用汉语与中国朋友交流。 2.时髦 and 流行，my personal idea is that 时髦be used in oral Chinese(or a little informal) mostly, but流行 be used in writing Chinese and more formally. Also, 了解 and 理解 be used in informal and formal situations. 3.熟练 and 擅长: 熟练 means be experienced. eg. 别看我是一个老外，我包饺子可熟练了; 擅长 be good at...eg.西方菜与中国菜相比，我更擅长做中国菜。（在厨艺方面我更擅长中国菜。） I am not sure I give you a clear comprehension, but I think I can understand you when you use those synonyms, even for us, we use anyone on a suitable situation. I hope my bad English don't make you confused.