there are a few high level buildings that can make it go faster. However, by the time you can build them, you have pretty much built everything in your city. The best option are champs with the administrator trait. they make stuff build 10% faster, and i am pretty sure they stack, so get a couple in one city and it builds real fast. But there is no hurry option, if thats what you mean.

Yes there are 3 ways to speed up construction.They each give a 25%  boost. These are for Kingdom I don`t know about empire.

1. The 4th level enchanment Magical Hammers.

2. The Construction Yard building. You need to research Construction which comes after Production.

3. The Guild Hall building which comes from the Guilds tech.

They all aren`t that hard to get if aim for them. I find them very useful and they are an important part of my win in 250 turns strategy. They allow you to mass libraries very easily. With all 3 it`s a Library every 2 turns.

Empire players also have construction yard, and magical hammers.

In addition to what has been said above, you can also (and should!) recruit administrators that reduce the time by another 10%. These bonuses all stack "elemental-style", which means if you get 25% from a spell, 25% from a building and 20% from champions, you're up to 70% (reducing a building that takes 10 turns to 3 turns).

I build these as soon as I can. I never stop building things in my cities.

Intentional. You can build on any tile that's in direct contact with the existing city.

@OP

Go here and fills up your boots.

https://www.elementalgame.com/hiergamenon/techtrees