Concrete – How to level the concrete foundations for the fence’s CMU block pillars

You have a couple things going on here: 1) The posts. an engineer would have to evaluate to be sure, but it's most likely that you will not be able to remove the posts without providing beams of some sort to span the space between the walls. Their irregular arrangement probably lines up with walls that they are supporting in the first story, which in turn are supporting the floor of the second story. 2) Clearance. Digging deeper to get additional clearance will be challenging, because you will have to leave the footers under the existing foundation in place, and not undermine them. This means you will likely end up with a floor that is a fair amount smaller than the existing space. Also, you will have to support the part of the house that are held up by the posts while they are being relocated/lengthened.

In either case, you will need advice from someone knowledgeable in building structure and foundations.

Overall, it may be easier/cheaper to raise the level of the house and add additional height to the existing foundation (if it is in good enough shape to take the additional load) than to dig deeper. A contractor that is experienced in this will know how to support the house while it is being raised, and you may be able to include new support beams to eliminate some or all of the posts at the same time.

I recently saw someone set a length of galvanized pipe in a concrete footer, and then bolt a pressure-treated fence post to the metal pipe. The galvanized pipe and footer should last essentially forever, and provide plenty of strength to support the fence/gate. The fence and gate can be replaced as needed. I thought it was a fairly clever approach. You might consider it for your application.

It's perfectly normal to have two gates without a center post, using a ground pin (often called a cane bolt) to hold the less-often used side of the gate stationary. The only downside here is that the gate will twist a bit more if side loads are applied near the top of the gate (e.g. wind, someone pushing on the gate), since the only fixed point is at the ground.

The longer the cane bolt, and the further up the gate it extends, the more support it can provide to the gate. Taking this to the extreme, if you were really concerned about the rigidity of the swinging end of the gate, you could make your own "cane bolt" out of a long section of pipe (perhaps 4 feet), and have it drop into a larger pipe set a foot or so into the concrete. That gate wouldn't go anywhere!