There are a lot of questions in there.
Whether it is 1, 5 or even 10 gallons you need to pitch the correct amount of yeast.
When re-pitching yeast, you only need about a quarter of the cake/slurry for the same volume and similar OG. Using the whole cake is way over-pitching, and in 1 gallon will noticeably take up a lot of volume.
Slurry 'should' be used within a week (stored in the fridge, without washing). I and many others have found no problems using slurry up to 4 weeks after harvesting.
Slurry will keep longer, but I would recommend washing and making a starter .... you may want to gamble; it is your beer. At 6 months, you will probably notice autolysis; the yeast could be washed, stepped-up and used at that point, but I would toss it.