It depends on the school that you will exchange to. Some will give you full access to everything and put you on their alumni database, whereas other schools will treat you as a visiting student and restrict access to careers services and networking events.
You have to find out about each school individually.
In terms of finding jobs, you can look for a job anywhere in the world providing the hirer is willing to sponsor your visa. FOr different countries there are different regulations since it may be easier to obtain a visa if you graduate from a school in the country you intend to work.
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