Eurail passes do not cover local transport like trams or metros, only intercity trains. Rail Europe is another company that offers similar European train passes.
You can use your Pass to travel on the national railways and some private railways in the countries where your Pass is valid. In some cases, these train networks reach airports as well. Check the full list here. The Pass even includes certain buses and ferries to make sure everything is within reach.
If you have an Interrail or Eurail pass you can use Eurostar between London & Lille, Paris, Brussels, Disneyland, Rotterdam & Amsterdam, but you must pay a special passholder fare.
On all trains covered by Interrail/Eurail: No, just as long as you can carry it. Be aware stowing away large suitcases on busy trains can be a bit difficult, but there often are luggage racks. There are some exceptions on “low-cost” trains, that I know: Ouigo (France & Spain) and Avlo (Spain).
First class also has wider seats and aisles, and is more likely to have amenities such as air-conditioning and power outlets (though outlets are still rare on Europe's trains, in any class). While first class is less conducive to conversation, it's more conducive to napping.
Interrail Passes can only be used by European citizens and permanent residents of Europe. You'll find the full list of participating countries below, plus loads of other useful information. If you're a UK resident, Brexit doesn't affect the Interrail Pass. You can still purchase and use one as normal.
What about Freedom Pass holders? Freedom Pass holders can travel across the entire length of the Elizabeth line free of charge, even to stations like Iver and Reading that fall outside the London Fare Zones area.
A 1st class Eurail Pass is more expensive than a 2nd class Eurail Pass, but it also gives you access to seats with more space and extras that can even include food and beverages. Check out our complete overview of differences between 1st and 2nd class to find out everything you need to know.
Because some trains are more expensive than others, or historically have received less income from Eurail/Interrail to cover the large amount of passholders making use of those trains (Spain and France mainly). Reservations are usually a fraction of the cost of regular 1st class tickets, with some exceptions.
You can hop on and off most trains as you please with your Eurail Pass, but some trains ask you to buy an additional seat reservation before you can jump aboard.
Bus / Coach. Taking a bus from London to Paris is usually the least expensive transport option. While not as fast as a train or flying, it is an easy way to get between the two cities.
Rail Europe is an official reseller of the tickets and passes that Eurail creates. Interrail is the same pass but for Europeans only; Eurail/Rail Europe is for non-Europeans. While Eurail also sells the same pass as Rail Europe, Rail Europe often sells these passes at a discounted price.