Alternative universes without max speed and with absolute time I'm not asking of something real but something mathematically possible.
Is it possible to do a math model of an universe (not ours) without max speed and without time dilatations? What would be the problems of this universe?
 A: Mathematically, such a universe is perfectly self-consistent and was studied as the dominant model for about two centuries: Newtonian mechanics. In many circumstances that model even does a good job representing nature. However, it does have a limited domain of validity and becomes rather egregiously wrong in certain regimes.
A: If you're looking for an answer that grants deep insights into possible realities, you've asked the wrong question. Practically the only thing physicists or physics students do is to make up model universes. That is, we populate some arbitrarily isolated space with some mathematically defined characteristics. We assign it mathematical rules. The we do math and make some predictions.
To be precise to the point of throwing away common sense, Dale's answer isn't literally correct: Newtonian mechanics is a set of functions that we import into a model, not a model in and of itself.
Here is an example of a model that satisfies your stipulations.
"Suppose two point-masses A and B isolated in free space*, with no net charge. Suppose that Newtonian mechanics govern all interactions. Let the displacement from A to B be $\vec r_0$. Let the initial velocity of A with respect to B be $\vec v_0$. Let the mass of A be $m_A$. Let the mass of B be $m_B$."
*by which we actually mean, "let's pretend that A and B are the only things in the universe"
Not that we need to use Newtonian mechanics. It might be useful to use a universe with only one spatial dimension. If you want we can get rid of time by turning time into a spatial dimension (the block universe model) then there's no such thing as speed at all, let alone max speed. If we don't mind getting nonsense results, we can even use nonsense rules. Suppose $\pi = 9$.
A: As other answers pointed, this is the universe of Newtonian mechanics... mostly.
It has few problems that not only limit the model applicability to our own universe, but make it self-inconsistent in the first place.

*

*Does your universe have boundaries or not? If yes, how do they behave?

*Is your universe more or less homogenous, or you have a single/limited number of stars in it? How about seeing a star in every direction you look, in the unlimited case?

*The power of interaction - if your interactions are instant, your fields need unlimited energy (you need to "shake" the field in the whole universe at once) or you throw away the concept of energy altogether. Or your interactions get limited in range and magnitude by other means. Inverse square law of anything is impossible when applied to the whole universe.

etc, etc, etc...
A: The problems of this universe depend on what are the exact details of the universe. If you are asking about an universe where EVERYTHING else is same except there is no max speed or time dilation, then the problems are exactly the same problems as with the Newtonian model , like others have pointed out
