99 times out of 100 sweet pea seeds will come true provided they are a named variety.
They are self pollinating and pollination occurs before the buds are open.
As to saving them, be guided by nature. You can tell when they are ready...the pods darken to eventually a brown colour, but you can cut the pods a little before that just in case they split. When you cut them, I store them in their pods in a suitable container for a few weeks in a warmish room to make sure they dry out before storage.
As to storing, any dry container....I use tablet bottles. If you have a glut of seeds then they can be stored in a freezer....some say for up to 10 years....for use in following seasons.

I say come true. When I update my blog there is a section on F1, F2 hybrids that show how seeds can end up any colour. So the pink/cream and pink/white seeds I saved 2 years have ended up all colours from white to deep maroon.

Gosh, Scrumpy, don't you know a lot? That's exactly the answer I needed. Thank you.

some named varieties are stable and come true. but many are not and you will get some variation. I always collect them when the pods are brown. I leave them in a paper envelop until I am ready to sow them either November or January.
you need to let seed pods develop fully on your morning glory too. picking immature pods [most plants] will mean the plant hasn't had the chance to convert all the chemicals it needs into the correct format for maturity/dormancy. the embryo plant may not be ready either leading to disappointing results.

Thank you both very much indeed.