You can use as many trains as you can find or manage on a chosen day-and as above, can leave actually the choosing till you hit the station. So if you really like a town, can stay longer and re-arrange all those pre-set plans. You can even use an overnight train that starts <24.00 till the end-though nearly all such trains also require an extra REServation.

depending on where/when you travel however, you may have to prebook/Reserve seats/space on fast trains-this varies a lot per country. This hence may restrict your freedom, but its mostly not really needed to panick about them and do it many monthes advance

You don't have to choose the travel days in advance. You only have to activate a travel day before boarding your first train on that day.

Thanks so much for your response. Just another quick question re. The flexible pass: so I have to book those days that I wish to travel when I actually purchase the ticket? Or can I just show up to a railway station and hop on (using one of my travel days)?

The travel days on flexible passes, i.e. those with X days within Y months, can be chosen freely within the validity period. 10 days in 2 months means you can use the travel days on 10 dates that you choose within those 2 months.

There are also consecutive passes: 15 days, 1 month, 2 months and 3 months. These passes can be used on all days in the chosen period.