It seems like it's possible to pick and choose whichever mission you want to do in a current chapter. Was there anyone who skipped all the missions and of the Voliir chain during the weeks it was considered the current chapter except the one that would give Sehrin? If yes, are you allowed to do the other chapter missions that you've skipped later?

Yes you can choose which parts you wish to complete(so long as they're not already archived), for example if you skipped this current fortnightly mission chapter, you won't be prevented from starting the next chapter.

However, once the missions are archived, you will need to complete the missions by chapter order.

Also, your not actually able to complete the end chapter of a mission until all the preceding chapters have been completed. So with the Sehrin chain, even if you skipped just one chapter, you would need to complete that first(once its archived) before you could access the mission which gives the Sehrin Bioship Ally.

Thanks for clarifying. So say I did a few of the Voliir missions, say the 1st, 3rd, and 5th (I don't know how many there actually are, but assume the 5th isn't the last one) before it was archived. When I access the archived Voliir missions, do I start from the 2nd mission, and then move onto the 4th, and then the 6th?

and when you do something like that, it will show you the mission screen for the part you're skipping, and it will have the 'next mission' box ready for you, i just went through 2 or 3 parts of the volliir chain and skipped the majority of the middle that i had already done.