1. Strictly speaking, "gather" in this sense means to slowly accumulate information from many different sources. You might read several newspapers, listen to the radio, watch the news and have conversations in the pub, and from all that gather that the war in Iraq is not going exactly as George Bush had hoped. However, so many people now use it in the sense you use it, that it's probably not worth trying to remember the difference.
2. "Deduce" means something slightly different; it means to use logical reasoning to come to a conclusion. Sherlock Holmes described the process of deduction pretty well: he said that once you have eliminated the impossible, whatever remains, however improbable, must be the truth. The process of deduction involves crossing off the list anything that is completely impossible, until you only have one possibility left.
3. Some people do confuse "imply" and "infer", but in error. In your sentence, Susan's smile implies she got the job; her boyfriend infers the fact from her smile. So your sentence is actually incorrect.
Actually, a more common error is for people to say "infer" when they really mean "imply".
- For Teachers