Upvote:2
What does "the processing of your application has not been straightforward" mean?
This means that they have had problems to assess if your application should be approved or not. Most likely because you have previously been refused a visa and therefore they wanted to do extra checks on you.
How long will this take? I have an urgent flight to another country next week
Their 2nd email says that you must submit your passport within 28 days of that date of that email. And that once submitted it will take approx. 5 days to process it (plus postage time if you send it via post/courier).
I would suggest that if you have a flight next week, that you submit your passport after you return (I assume from your text that you are only gone for a few days/1 week). Otherwise you will not get it back in time.
The 1st email contains some text which is not relevant to you. It contains standard text which is sent to most/all applicants. So you need to find only the parts which are relevant to you. Which I have done here.