For 2-C, how many universes for each? For Tier 1, what dimensionality for each?
Number of Universes
As seen below, the number of universes was infinite before the Crisis on Infinite Earths which reduced it to a singular universe until the Infinite Crisis which brought back the multiverse with a set number of fifty-two universes occupying the same space at different frequencies, but there could be more with the discovery of the 53rd universe. Here are Kendra Saunders' own words after studying the multiverse map: "We know of fifty-two, we believe it to be the set number." She talks about known universes, suggesting that there may indeed be more universes unknown to anyone in the multiverse that may or may not be separate possibilities stored somewhere in Hypertime.
Geometric and Temporal Dimensions
As for the geometric and temporal dimensions, the multiverse is described as having a 4-D space-time continuum. This was the case for Grant Morrison's approach on the DC Cosmology that was later adopted by Scott Snyder, as evidenced in his Justice League run. In Mr. Mxyzptlk's own words: "The multiverse, as you live it, puny heads, exists in four dimensions..." He explained to the Justice League that they experiences the first four dimensions which, in Snyder's words, are point, line, depth, and time.
The Bleed
The interdimensional between universes. It was described as the substance of life where the House of Heroes rotates through the fifth-dimensional axis in a fixed point in the multiversal structure of the Orrery of Worlds. Four siphons have been drilled in from the Monitor Sphere to the Orrery, to permit harvest of the miracle Ultramenstruum, known also known as Bleed, from the universes of the multiverse, that the Monitors refer to as 'germ worlds.'
Morrison's Final Crisis: Superman Beyond depicts the Bleed to exist in 4-D. These are Monitor Zillo Valla's own words: "We'll traveling through the Bleedstorm space between the universes... But you'll need to upgrade to 4-D vision to truly comprehend what you experience."
Sphere of the Gods
An archetypal realm outside of corporeal reality, at the edge of the multiverse, and the homeworld of all gods, deities and magic. Although the inhabitants of the Sphere of the Gods exist on a higher plane of existence than those of the Orrery of Worlds, they exist in 4-D.
To summarize, the local multiverse is 2-C. There are 52 universes, each existing in 3-D and when you leave them you enter the 4-D Bleed between and around the universes. Every other universe whose exact number is infinite are stored in Hypertime which exists outside of the local multiverse.