Malus x domestica

Malus x domestica

Greetings. We just bought an apple tree this weekend, Malus x domestica, "Red Delicious". The tag claims it is self-pollinating. We were content with this, until I started reading information on the internet which claims most apple trees are not self-pollinating, and that even those that claim they are will benefit from cross-pollination. Does anyone have any thoughts or experiences with this? We have what we think is a crab apple tree in the same yard where we put the new Malus. We were planning on either destroying it or digging it up and giving it away. But, I also read that crab apple trees are an excellent source of pollination for most Malus trees. This is cool, but what worries me is, I'm not entirely sure how fruiting trees work, but I'm guessing that if my new Apple tree which is supposed to bear big fruits gets cross-pollinated with a smaller variety (i.e. crab apple), that my would-be big apples will end up being smaller. Again, thoughts and conversation are welcome.
plant i.d.

plant i.d.

Room/Bathroom in Carmel

Room/Bathroom in Carmel

flower identification please

flower identification please

My room!

My room!

garden centre

garden centre

plant ID halp?

plant ID halp?