How long does it take to find a male partner and to get everything sorted?It can be a life-long search

, it's just knowing the right people and being on the right places that will make the search more easier/faster.
As to how long it takes to get everything sorted: it depends on how much both are willing to compromise in order to make the partnership work.
How likely is it for the male dancer from abroad to relocate to england?
Only if they originally intend to move abroad. IMHO it's very unreasonable to ask someone to relocate.
How hectic is the life of a competing dancer?
Again, this depends on how active you are in the dance community. If you want to attend every competition out there, the time invested in it (training, general preperation, travelling etc.) could account for a job.
All my luck to your girlfriend, I know how hard it is to find a partner! 
"Carpe diem, quam minimum credula postero." - Horace