Keep in mind, the story is told pseudo-linearly. I'll list this stuff in mostly linear order.
The Cult of Skaro created an intelligent time machine designed to appear as TARDISes during the Time War. It's capable of analysing timelines.
The Dalek Prime Minister, Eternal (who is apparently decades old), Supreme, Scientist, and such appear in this story.
The Doctor believed the Daleks would be weakened after Oswin erased their memories. Instead, the New Paradigm were incensed by their otherwise total victory over the Time Lords, and actually became stronger than ever—a sort of 'reborn' Paradigm, with the same leaders/command structure. It's also confirmed that the New Paradigm and New Dalek Empire are the same thing.
Despite apparently being
stronger than their Time War levels, they were still concerned at the prospect of fighting the Time Lords. It's also implied their overall temporal power and ability to create pocket dimensions is still greatly diminished.
Pathweb communication is instant, and allows them to swarm ground enemies very quickly. The Doctor and Medrüth abominations try to compromise the Daleks' purity through the Pathweb, but it doesn't last for more than a few minutes before their hatred overcomes it. Imposing direct mental changes on the Daleks doesn't really work in general.
Their mind probes were 'strip mining' The Doctor's mind.
They have their own version of the Special Weapons Dalek (see
here) that can kill energy-absorbent Medrüth abominations (created by an alien mutation known as The Surge) with 3 shots, whereas normal Daleks can't really even harm them with large volleys.
A Dalek fleet destroyed Medrüth in seconds.
Dalek forces swarmed 'every sector' in 'greater numbers than [humanity has] ever seen' during the opening of their war. It's implied that they stomped the Space Security Service and Shadow Proclamation in a very short time, killing millions and destroying hundreds of worlds as quickly as The Doctor could save one world. The universe was apparently dying after some time.
The Doctor described the invasion as being on the same scale as the Time War, and was so badly outnumbered and outgunned here that he believed they could destroy Daleks for millennia without actually stopping them. Though this is contradicted by later statements that the Daleks only number in the millions.
The Supreme believed a Dalek fleet could destroy the TARDIS, but this is never proven.
The Daleks would've won the war handily and completely in this timeline, with literally 0 chance of failing at conquering the universe according to The Cult of Skaro's time machine. However, the main characters cut a strand of the Web of Time, allowing them to create a new timeline where the Daleks lost and their main forces died.
In a potential timeline that The Cult of Skaro's time machine planned to create, The Surge would've become ubiquitous throughout the universe, leading to a Dalek defeat in approximately 3 billion years, albeit at the cost of trillions of lives (including The Doctor's) and entire galaxies.