That has happened every time I've tried to launch Skyrim today. Is the Steam crashed or whats the problem why Steam always stop answering when it's trying to connect your Steam-Account?

because steam ultimately svcks and is the downfall of future pc gaming. Its [censored] trust me.
But seriously i dont know, steam always has problems so it could be anything. that really svcks though

You can try to play in the offline mode. Open Steam and select Go Offline under the Steam.

Has your computer accidentally blocked steam with a firewall?

Check to see if you have an internet connection... Post back if you don't, and I will e-mail you instructions how to get back on the net... Wait.. scratch that... you are online... (JK, I am not that dense. Was a joke, I swear! Seriously... )

In your control-panel, or on your network icon... Select the firewall tab and make sure STEAM is ALLOWED to use the net. (WIndows may have auto-blocked it, just now detecting it as a potential threat, accessing ports on your internet. Or someone may have selected, YES, Block this program from accessing the net. Or it is randomly blocking it... Or the servers in your location are down/busy.)

Steam is allowed at firewall and I have tried also offline mode which didn't work. I also chanced Steam to have higher priority which didn't work either.
When I tried to launch it in offline mode it said it can't connect to Steam-Net. Never know what it means.

In order to use Steam Offline you must first connect to it online, I know it's stupid but that just the way it works. I think it's to do with connecting to your account and stoping you from loging in twice on different PC's.

I have been online in Steam several times so how can this be the problem? Does that mean I need to do something online before getting offline and then do something offline before getting back online? If it is so what's the meaning of offline mode at all? I thought it's there for this kind of cases when you are not able to get Steam online.