Is it plausible to change my major from pure math to applied sciences when applying for graduate school?
How possible is it for me to change my major when applying for graduate school? What kind of school can I hope to get into (preferably in North America or Europe)?


This isn't all that uncommon. In the CS Msc programme at my university (Leiden) for example, we get a lot of people coming in from Statistics. The emerging field of Data Science has caused Statistics and CS to become much more closely related fields.

Exact requirements will probably vary by university, but at least in the EU the system is set up to make it possible for people to combine pieces of education from multiple universities. A BSc in mathematics together with some catch-up CS classes will probably get you in the door in a CS master. 

That's not the of the story though. Individual courses often have their own requirements; a masters' course on advanced data mining might require prior basic data mining knowledge. But that doesn't mean you have to have taken the data mining class offered at that university. Our CS master attracts a lot of students from other universities. The requirement just means that if you don't know anything about data mining yet, you're going to get thrown into the deep end.

Since these requirements are mostly "you should already have a foundation in", not "you must strictly have this particular class", you could also fill in those blanks with online courses or reading relevant handbooks.


  Is it true that other departments welcome pure math students, as is said by the professor mentioned above? Would an admission officer focus more on my advantages or disadvantages?


What the admissions officer focuses on will differ from institution to institution. However, you should not be too discouraged by lists for formal requirements. People move from all kinds of places to all kinds of places, so partial matches are extremely common. Often you should be able to come to an agreement along the lines of "You already match ABC, but you need to pick up XYZ as well before you can enter". 

Me for example, I wanted to switch from History to CS. For CS I needed a particular flavor of high school math as an entry requirement, but the remedial course they usually used was already fully booked. I found a remedial course at a different university and proposed that one, and they accepted that.

So approach the advantage/disadvantage discussion as a discussion where you look for a mutually acceptable solution. Be imaginative and constructive.

Right now, about halfway in the current academic year, is actually a good time to do this. If you can come to an agreement with regards to requirements, there is still a whole semester to take some remedial courses in a university or an online course that the admissions officer considers acceptable.


  What other fields can you suggest?


As a CS student I'm a bit biased of course, but if you want to apply math, I'd definitely consider a  CS Master. Machine learning and data science tends to be a significant part of that, and a strong math background is quite useful there.

Apart from the hip neural network side of things (which is much more about matrices than you'd expect), I would also recommend optimization/decision support as an area of study. This has a big mathematical component to it, which "native" CS students aren't always as strong in. In the field of natural computing in particular, there are a lot of people doing projects based on interesting proof of concepts, but lacking theoretical/mathematical analyis. That's something that a math background could help you with.