Hi, for Eurostar trains there you need to be at the station to go throw security and Police check 40-60 minutes.

For other trains depends how big the station is. Mostly some minutes before to be sure 15 minutes before, sometimes 1st class lounge is included in your pass. depends from the train company.

security and police checks are not common in Europe, except between UK and rest of Europe and security checks in spain.

The Eurostar queues at St Pancras can be quite chaotic, but they sort of manage them.  Don’t be shocked if you turn up for a peak time train and there is a massive queue stretching through the building.  The slightly good news is that they have people running around with signs saying “15:20 to Paris” or “1600 to Amsterdam”, so if you are tight on time and at the back of a huge queue keep a look out for someone trying to round up the remaining passengers for your train.

I don’t think they tend to leave people behind in the queue while their train trundles out of the station but you need to keep an eye out for those signs.

Off-peak may well be much different with little queueing, but my experience has been of chaos a couple of times.

For the rest of Europe (other than return Eurostar trains) you can normally just wander up to the platform with a few minutes to spare.  But, but, but, remember that some stations are massive so it could take you 10+ minutes to walk from one side to the other, your platform could be down a long corridor or somewhere out of the way, so the “few minutes” refers to you being at the platform.

Depending on the size of the station you may need to be at the station 10, 15, 20 minutes before departure.  I normally try to check out where my train will be departing from and get an idea (when I arrive) how long it will take me to get there for my departure.

You go through both sets of immigration at St Pancras when travelling to the Schengen Area - British and French - before entering the waiting area and then being called to board your train.

At Gare du Nord, unless you have something to declare (there may be spot checks) you can walk straight off the end of the platform and into the main concourse.

The same applies in reverse when travelling to the UK.

https://en.wikipedia.org/wiki/Juxtaposed_controls