This one is simple. All Right is correct. Alright isn't. A Lot is correct. Alot isn't. Alright and alot are considered substandard. Don't allow your writing to be substandard! :-)
All right, I'll come with you.
The setting was all right with him.
We used a lot of ketchup.
He worked a lot of overtime hours.
Authors/writers: Make sure you're on my list of authors!