Starfall
One of the most common issues with starfall is that players run out of time before they can complete the quest chains, and to be honest if you have the resources in store this is a very easy task to accomplish, for instance you need to gather or produce a set amount of items and at the same time produce some buffs in the forerunner.
So first forget about the gather/produce part of the quest chain - set the production up to make what is required - then do this again - so if you need to make 5 items - set up another production of 5 items - once this is done cancel the second set, now have a look at the gather and produce part of the quest chain - it should now be completed - so all you need to do now is wait for the original set of buffs to be ready and that part of the quest is done. you can do this process for almost all of the gather/produce quest chains - in a few instances you can simply take resources out of you star menu and add to mayors house.
 
 
 
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Between a rock and a hard place

Shipshape - make required items in PH and then wait 1 hour.

Collecting the clues - make 8 mote collecting kits - then make another 8 - see image 1, cancel the second set see image 2 and image 3, by doing this you have now completed the gather part of the quest, so let the first 8 mote collection kits finish being produced and collect the motes on your island,this part of your quest chain will be finished.

Set the course - (see subnote) we do this the same way that we did the previous part of the chain, set your production up to make 1 and then another 1, cancel the second one and then use the heading coordinate buff on your forerunner. quest chain now complete

Lets get cracking - nothing to make here - but we do need to either produces or gather some items - this is best achieved by either placing from you star menu in to mayors house or double trading - the same as a normal double trade you send the items and then buy them back

This will be a blast - here we need to make another 50 items, make and then use on the otherworldly hard rocks.

Getting ready - here we need to make the 5 scrapper kits, so set production up for 5, and then 5 again, cancel the second set of production.

Time to deploy - use the 5 scrapper buffs on otherworldly crystal formation

Look at them go - fully mine the deposits.

Altered states

Shipshape - make required items in PH and then wait 1 hour.

Collecting the clues - make 8 mote collecting kits - then make another 8 - see image 1, cancel the second set see image 2 and image 3, by doing this you have now completed the gather part of the quest, so let the first 8 mote collection kits finish being produced and collect the motes on your island,this part of your quest chain will be finished.

Set the course - (see subnote) we do this the same way that we did the previous part of the chain, set your production up to make 1 and then another 1, cancel the second one and then use the heading coordinate buff on your forerunner. quest chain now complete

Eerie Spires we need to produce 150 resonation canceling devices - so set your production up to make 300 and then cancel 150 of them, this will complete the gather or produce part of the quest chain, once the 150 resonation canceling devices are made - the quest will be at an end

Radiation sickness - use the resonation canceling devices

Business as usual - set up production to make 5 scrapper kits, then set it up to make another 5, cancel the second set - when the first 5 are made this will complete the quest

Mine you business - use the 5 scrapper kits this will complete the quest

The dust settles - wait for the pits to be fully mined

Fallen star mining

Shipshape - make required items in PH and then wait 1 hour.

Collecting the clues - make 8 mote collecting kits - then make another 8 - see image 1, cancel the second set see image 2 and image 3, by doing this you have now completed the gather part of the quest, so let the first 8 mote collection kits finish being produced and collect the motes on your island,this part of your quest chain will be finished.

Set the course - (see subnote) we do this the same way that we did the previous part of the chain, set your production up to make 1 and then another 1, cancel the second one and then use the heading coordinate buff on your forerunner. quest chain now complete

Mechanised Industry - here again we make the first set of items (5 required, then set up production for another 5) cancel the second set and wait for the first 5 to be made.

Roll then out - use the scrappers that you have just made on the otherworldly crystal formations

Tweaking and Improving - set up a production of 10 scrapper lubricants, then set up another 10, cancel the second set and wait for the first 10 to be made

Final Test use you lubricant on the scrappers, 2 hours later do the same again - now keep adding lube every 2 hours until all shardes are mined.

Subnote
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Rooting out the problem

Shipshape - make required items in PH and then wait 1 hour.

Collecting the clues - make 8 mote collecting kits - then make another 8 - see image 1, cancel the second set see image 2 and image 3, by doing this you have now completed the gather part of the quest, so let the first 8 mote collection kits finish being produced and collect the motes on your island,this part of your quest chain will be finished. then forget about this quest chain until it expires (for high level players and for low level players you get no star shards from this quest so unless you really want the xp, why bother with it).

If you decide to do that part of the quest chain - then apply the same method as described for the other quest chains bearing in mind that it has 3 main parts that take 12 hours each.