What's the climate consequences of a planet with these characteristics?

Question

I'm designing a new planet, but I'm having some troubles figuring out the climate.

• The planet's rotation axis is at a 45° angle relative to its orbital plane, and each rotation takes 24h.
• The planet's axis tilt has a cycle equal to the planet revolution around its star [That should make it so that the southern hemisphere is always the one closest to the star]
• The planet's orbit is elliptical [Has seasons. The tilt synchronised with the revolution should mean warmer winters to the South, and colder summers to the North (warmer than the rest of the year)].
• The planet has a deep trench/canyon at its equator, running around the entire planet, deep enough to reach the inner mantle (not the core).
• [EDIT] Something that might be worth adding: on both sides of the canyon, I plan on placing tall mountain ridges.

Given these informations, I need help figuring out the climate zones and the the weather events on a planet with those specifics. In particular, how would such a deep rift at the equator influence the climate of each hemisphere?

Here's a couple of simple drawings to show you what I have in mind:

Answer 1

If this planet could exist, which it can't, it's effectively tidally locked, the southern hemisphere will be unbearably hot and the northern hemisphere will be frozen solid, there will be a thin zone of habitability near the equator.

There are two reasons this planet can't exist in our universe:

First - "The planet's axis tilt has a cycle equal to the planet revolution around its star" this would melt the entire planet before it made a full orbit. The energy required has been worked out on this stack before, it comes in at something like the lifetime output of our sun, every orbit. The waste heat from this would liquefy the planet in approximately 7 months, vapourise it in less than 18.

Second - "The planet has a deep trench/canyon at its equator, running around the entire planet, deep enough to reach the inner mantle (not the core).", um no, the mantle is plastic-liquid, highly viscous but not competent. In short the crust will not support a trench that goes below the Mohorovičić discontinuity, in fact you can't support a trench even that deep into the crust unless you want to invoke magic.

So, given that this planet can only exist as a product magic, you can have any weather you like.