What can run but never walks, has a mouth but never eats, and has a bank but no money?

What is the next letter in the pattern: J, F, M, A, M, J, J, …?

I am small, brown, and squirrels love to hide me. What am I?

What has many keys but can't open a single lock?

What has a thumb and four fingers but is not alive?

What goes up when rain comes down?

I'm light as a feather, but even the strongest person can't hold me for long. What am I?