You are welcome to stay here. (natural) I welcome you to stay here. (not natural, but doesn't sound wrong) I invite you to stay here. (more natural, fairly formal.) I welcome you to my house. (ok) Welcome to my house. (more natural)

Generally, no, it isn't. There are a few special cases where it might be. John gave some good examples of similar phrases. Chinese people have a tendency to misuse 'welcome' in English / western culture. I assume they are directly translating something that is said in Chinese, but doesn't translate directly. One example I often hear is 'Welcome to China', or 'welcome to "my city"'. We don't actually say 'welcome to a place', unless you have actually arrived there. The best translation for that would be something like 'You are welcome to visit XXX', or "I welcome you to come to XXX". But even those still sound a little strange. It just isn't something we usually say. John's example of 'visit us' is more specific, as it is an offer to come to someone's house.

Here are some correct and native examples that are very similar: You are welcome to come visit us anytime. He is welcome to take whatever he likes. We welcome your assistance on this project.

Please note that sb and sth are dictionary-only abbreviations. We don't use them in normal English. Some native speakers wouldn't even understand what you mean.