I think the three questions you listed down are questions you can only answer for yourself . But here's a train of thought anyway .
The lady seems to be more interested in focusing on her career right now more than being in a committed relationship . Or at least in a committed relationship with you ( sorry to be blunt ) . Give her some space , to achieve her dreams . Stay in contact . Perhaps you will find a time in the future where she wishes to become in a deeper relationship with you . At that time you may wish the same or you may have moved on .

You feeling burnt out and wondering if you need to add some hobbies . In short , answer that with question three .

Question three . Not sure if you should take the job offer in another country . Only you can answer this , but it would be a great opportunity to deal with all three questions you have . Your 30 ,single and good at your profession , so no better time to do it . It will expand your mind and perspective . Give you life experience you will never get staying where you are . The change will take your mind off the lady and show to her that you also can move on and do interesting things ( likely to make you more attractive to her strangely enough ).
It could give you a new perspective and appreciation of your profession in a different , new environment . It will give you ample opportunity to open your mind to different hobbies , arts , cultures .

Leaving your country to work is not all sugar and roses . It can be hard and sometimes lonely , but it makes your spirit grow . In my 20's I went to Europe for three years to work . It was one of the smartest things I ever did in my life . I grew as a person , grew mentally and strangely enough also found love .
What do have to lose ?