Read to them!
Over and over, lots and lots of amazing books! They will learn all this stuff if you simply talk to them a lot, take them on outings to lots of different places and read to them. You don't have to formally teach them anything.
For this to work, you need to spend lots of time with them. It sounds like you're doing this and that you're a lovely aunt so well done you!
Remember that kids who recite all these things don't necessarily know what they're saying. Young children have very little understanding of abstract concepts so how would they know what seasons and numbers are if they simply recite them? Rote learning like this is useless - kids need to hear these ideas in context to learn and understand them.
This is where reading helps. Think about the difference between a child reciting 'summer, autumn, winter, spring' and a child who has read and loved and discussed a story about a child who, for instance, lives in a very hot country where it's effectively always summer. Learning without context = no comprehension.
With the alphabet, teaching the sounds is so much more important than teaching the letters of alphabet using their names. Teach this by all means but you can actually do a lot of damage if you neglect the sounds. These are THE most important thing.
A child who has an understanding of the sounds of letters and words has developed what we call phonological awareness. This is the most important predictor of whether a child will learn to read easily and naturally or whether he will struggle.
There's more info about this and about why poems and rhymes are so important in developing phonological awareness here:
http://www.best-books-for-kids.com/poems-for-kids.html
In summary, please don't mistake being able to recite lists of things for a sign of intelligence or a sign that the child will be a star at school. This is just not true. Reading to a child is the best way to make this happen.
If you're really interested in reading more about the importance of reading to children, have a look at these books and websites:
http://www.bookdepository.co.uk/book/9780143037392/The-Read-Aloud-Handbook=Best-books
http://www.bookdepository.co.uk/book/9780156035101/Reading-Magic=Best-books
http://www.memfox.com/the-folly-of-jolly-old-phonics.html
http://www.trelease-on-reading.com/
http://www.best-books-for-kids.com/reading-to-children.html
http://www.youtube.com/watch?v=M4Lv9KRXV0Y