1) At Paris Gare-de-Lyon arriving ½ hour before the train is plenty. There is no check in. The platform number is usually shown on the monitors about 20 minutes before departure. Just make sure you are on the train before it starts moving :-)
2) If you have a print-at-home ticket you do not need to have them checked before getting on board. Just get on the train. In theory they say you require proof of identity (the credit card with which you booked the ticket). In my experience they never ask for it. So long as you have your print-at-home ticket, and nobody else is saying that is their seat. It is OK.
3) Within Switzerland it is "turn-up-and-go". So buy your ticket at Basel when you get off the train from Paris. Price is Basel to Luzern CHF 32 (full fare 2nd class), and take the next train (3 per hour, journey time 1-1½ hours).
4) Here is a problem. Luzern to Basel is CHF 32 "turn-up-and-go" no problem. But Basel to Paris is cheaper if you book in advance. Book your tickets Basel to Paris ASAP (if not sooner) :-). French TGV trains MUST be booked in advance and are a lot cheaper the earlier you book them.
Conclusion: Each railway company has a different set of rules and a different pricing strategy (just like each airline). You just have to know the rules. In most cases there is one national railway company (and one set of rules) per country, which makes it easier.
