For the shape and structuring of the portal it would most likely work off theoretical structures of wormholes as being a three-dimensional hole in space-time, this being a very hard shape to wrap your head around as all holes we normally encounter are 2D (like drawn on paper) or just form a cylinder/tunnel if they are in a 3D structure like a wall or floor). Being a spherical hole the inside will be constantly shifting and changing due to each side trying to continuously show a 360 degree view of what is on the other side. (a good exmple would be the wormhole in the interstellar movie)
The border of where the portal ends and our world begins could vary depending on how it was produced. If it was produced by artificial means like a developed society that is experimenting with inter-dimensional travel it will depend on how developed they are and how much experience they have with making portals. For a less developed and knowledgeable civilization they portal could be very energy inefficient (like most prototypes are) this could make the broader unstable and irregular looking like it is threatening to collapse or pop (constantly shaking and trying to contract and expand in different areas), it could be any shape but with a general sense of roundness to it. If the civilization is advanced and has experience then it would be much more stable and the boarder would be smoother and almost perfectly wound a spheres are the most gravitational efficient shape.
For naturally occurring portals they would most likely follow the same design as one produced by an advanced society. This is going by old string theory theories proposing their being a 'cosmic string' that holds open wormholes to keep them perpetually stable, although i don't know how this would work for inter-dimensional wormhole formations as the 'strings' connect places within the same universe.
Now for the main part of your question on what the affects a portal to a low energy dimension would cause to the surrounding area. There are three things to consider for this question.
1. What is the difference in energy content between our universes or areas where the portal is located:
If the energy level is very low in the other universe compared to our universe then energy will be leached from our universe. depending on how great the difference is the surrounding temperature can drop tens to hundreds of degrees in seconds and continue to drop as more and more thermal energy is leached out of the surrounding area. this will cause water to freeze and if the temperature drops enough the air could liquefy or even deposition could occur if the temperature drops too quickly where the air literally turns into solids.
This would happen inversely on the other side of the portal where everything gets hotter.
The portal itself will most likely be very dark as no light is coming through and is just passing into it and not being reflected off.
2. Where is the other side of the portal located:
If the portal is placed in the vacuum of space the atmosphere on our planet will being to quickly be sucked into the portal like an actual vacuum. The air will flow in a constant rate towards the portal, depending on it's size it could be a constant gentle breeze or full force hurricane winds, this continuing until there is no atmosphere left on earth.
If the portal is on a planet the size of the planet and its' own atmospheric pressure will affect the rate of gas transfer through the portal. If the planet is large with no atmosphere our atmosphere will be sucked through the portal to fill empty space and even if it cannot be completely filled the amount of air we have on earth will shared between the two planets even distributed by which is bigger. If the planet is smaller than our it will still take some of our atmosphere but leave most of it with us.
If the planet has lost of atmosphere, more than ours then gas from the opposites side of the portal will spill into our world. This can be problematic as gases coming in might be completely toxic to us like pure chlorine gas or completely fundamental different and could act as a toxic cloud of gas spreading over the entire planet.
No matter how much atmosphere the planet does hold the gases will constantly travel back and forth through the portal until a balance of pressure is achieved on both planets.
3. Does gravity travel through the portal boundary:
If gravity is able to move through the portal then this will be the biggest issue for everyone. on the smaller side of things light will start being towards and around the portal.
On the upper end of the more realistic spectrum all matter on the other side of the portal will start pulling on all matter on this side of the portal. This will cause will cause massive quantities of matter to be pulled though the portal. If our collective universe is heavier then the matter in the other universe, then matter will be pulled though the portal here, the closest objects first and those further away will start accelerating towards our side of the portal, gradually getting closer to near light-speed speeds.
If our universe is lighter than the other then the portal will act as a black hole with the mass of an entire universe behind it. This will destroy earth in a faction of a second, followed shortly by the sun and the entire solar system. It will cause everything in our universes to start slowing down and accelerate towards the portal till our entire universe is empty of anything with mass.
This would most likely produce something like a big bang but over a much longer period of time.