20C/68F is the minimum temperature you should aim for; the developer will start to fail (poor blacks) at 18C/65F. Aim for more like 25C/77F; with the bonus that it keeps your hands warmer. It will oxidise and die faster though.
Multigrade, like any dev, can oxidise but it doesn't seem to do too badly in the bottle. I have a decade-old 5L bottle of it that I scored for free and it's dark apple-juice yellow; I use it at 1+6 instead of 1+9 out of conservatism and it works perfectly. Since your developer is only pale-straw then it should be totally fine.
Stated capacity is 100 of 8x10 per 1L, which means about 100 of 11x14 in your 2L assuming RC paper. Half that for FB. Either way, you shouldn't be running into capacity issues.
My guess would be cross-contamination despite your care or oxidation in the trays; it only lasts a few hours. Try giving all the trays, graduates, tongs, etc a really good scrub in hot soapy water, and make sure you have one specific tray that is dedicated for developer use.