"skriva" is general and could be with any method possible, while "type" is more specific, so translating to "write" fits better. When the method is not important, type can be translated to skriva (since Swedish has no specific verb for that), but when the method is important a different phrase is needed. For a typewriter (skrivmaskin) one can use "... skriva maskin", but for a computer/keyboard I cant think of a shorter way than "... skriva på datorn/tangentbordet".
It's not a deponent verb, it's a particle verb, but you're right the particle must be stressed. I think the Voice does a pretty good job here. We usually recommend forvo.com for listening to natives saying things, but I can't find anything suitable there in this case. There's also a super helpful user who has recorded many sentences, see his discussion topic here: https://www.duolingo.com/comment/5581851 He has a recorded the sentence Hon tycker om henne 'She likes her' here: http://vocaroo.com/i/s0xKEJzUWVJS