With a Schengen visa you can travel freely within the Schengen area. No border checks generally occur, and if they do they might check your Visa but will not deny you entry if you have a valid Schengen visa. 

It mostly depends on the countries and the trains, but in some countries (France, Spain, Italy) and on some trains (Eurostar, Thalys, TGV, all night trains) seat reservations are required (costing between €4 and somewhere around €50, depending on the train and route)

With the Schengen visa you can travel in all Schengen countries. 

https://www.schengenvisainfo.com/schengen-visa-countries-list/

Other than the freedom of movement in the Schengen area you will meet with normal border controls, often an outward and an inward  inspection. Sometimes leaving a train at the border to be checked and then catch the connecting train, or occasionally an onboard inspection.

If you include the UK in your journey your passport will be checked by Schengen border control and UK Border Control staff before boarding the Eurostar, but not again on arrival. 

But again, border checks are very, very rare.

Absolutely no need to be ages before departure in the station for an international train for formalities (with the exception of Eurostar). Being 5 to 15 min in advance in the station suffices in 99% of the cases.

The only border within the Schengen zone where a very short check seems to be systematically in place is the German-Danish border at Padborg, but only if you enter Denmark.

Reservations are not mandatory for 90% of the trains all over Europe. Only for some exceptions like @Schelte mentioned (and probably you’ll travel a lot on these trains). The community has an excellent guide on how to get reservations. They’re completely separate from the pass btw. Best read it thoroughly.

In most cases reservation free alternatives exist, if you don’t want to be bound to specific times. Those options are usually a bit slower though.

The Eurail pass does not cover any busses (unless it’s a rail replacement bus, due to planned engineering works or an incident disturbing rail traffic for a longer time).

OZzies do not even need a special Schengen visa for short duration touristy stays-just show passpt when enter the first nation-likely from the plane. Even as we do need to some pre-clearance. It works just like these OZ states: once in Schengen youre free to move. About any train that goes over borders will also first serve stations INland so there is not even a distinction between these pax.

Which is very much same-same as I remembered from going from MEL to SYD on a train -once, long ago.

I assume you have seen this page.
https://www.smartraveller.gov.au/before-you-go/the-basics/schengen

As you see from the previous posts, borders in Europe are reasonably easy to cross by public transport. All you need for most countries is your passport as shown in this article, and quite often border transit is totally transparent. The Schengen countries have a maximum limit of 90 days stay in any 180 days so keeps a record of entry and exit from Schengen for citizens of non-member countries.