First of all, there are many trains departing from Beijing Railway Station to Shenyang everyday. So, if you will not travel in peak season, I think you could purchase the train ticket once arrive in Beijing, at least one or two days in advance.

Of course, it is assured to book tickets via agent in advance. This website does have this service, please ask them for details.

2. Shenyang is not very large for travellers. So, I think it will be fine to visit by taxi, cheap and quick.

Thanks so much Mr. Jamie for your quick reply.
I looked at the train booking site. It seems very easy to use! After selecting train/date, it looks like we have to book at least 7 days in advance... We'll surely try next time. Cheers! :)

Thank you for the useful information. I have been studying in Shenyang for almost 4 months now and soon my boyfriend will come here as well but I have no idea about some crutial things we'll have to do when he comes. It'd be of greatest help if you could tell me what kind of job it is possible for him to get here and how (he is a 25 years old Greek, perfect English and many other skills). And another thing is we want to rent an appartment, would you advise any good company to work with in order to find a good and not expensive one? (the 20-45 thousand RMB that you wrote for 6-12 months - is it a flat in the centre of Shenyang or in the suburbs?) Thank you beforehand!