Free WIFI in Europe

Impossible to generalise. Some large big city stations have WiFi, of varying quality and varying coverage. Local stations, never.
Just because station A has it and station B is larger, doesn't mean station B will have it, totally random. If you find it, treat it as a lucky bonus.

Same applies for trains. Some have, especially if they have recently been upgraded, most don't. Even if it is in the train, if the train goes through an area with no mobile coverage, hard luck.

Finland's trains have on-board wifi.

Sometimes yes, sometimes no. Same for airports (airports always have wifi but sometimes it costs). In every town I've been in you can easily find cafes with free wifi for customers, and most hotels offer it free to guests. Wifi won't be hard to find, but whether it is in the train station specifically will vary.

Most hotels and restaurants will have free wifi. Even had a couple of cities that had free city wide. It is a hit or miss outside of most restaurants and hotels but we have found that this is more than adequate of us.

Thanks for all the help. sounds like the same situation in North America