The questioner said, "As the 3/15 deadline has just come to an end, I was curious to see if you need help with your 4/15 clients. I have a lot of availability and am happy to help."
Question 1) can you say you have A LOT OF AVAILABILITY? 2) can you say "a deadline has come to an end?
Everything you said, almost certainly will be understood by the other person. That is good. But there are better ways to say these things.
We don't say that a deadline has "come to an end." We say that a deadline has passed. One might say that the period of time ending on the deadline has ended. But the deadline itself is one specific date, not a period of time. That specific date doesn't come to an end. It simply passes.
As to the phrase "a lot of availability," I probably would not use that phrase. I would say simply, "I am available." I understand why you might want to say "a lot of availability," because there may be some times when you might make an extra effort to be available. In view of this, your choice of words seems very true and correct. But it is such an unusual choice of words, that it appears inappropriate in a business situation.
Still, I think that your original choice of words and phrases almost certainly will be understood.