1. If you live in Europe, look up Interrail and if you live elsewhere Eurail. It can be purchased anytime. A mobile pass can be activated within 11 months and for a paper pass you need to choose a starting date (and wait until it is delivered home).

2. Usually bookings are open 90 days in advance, sometimes more, sometimes less. Be aware that not all trains will require a reservation.

Paris to Switzerland yes : the direct TGV Lyria option has an expensive reservation fee, especially for 1st class passengers but there are options to avoid it.

within Switzerland no

Zurich - Milan yes 11€ on ÖBB website

Milan - Venice yes 10€ on ÖBB website

3. Usually on the companies operating the trains but there are exceptions : for Italy it's better doing it on the Austrian Railways website ÖBB (don't ask me why)

But, and it's a big but, I'd seriously consider buying regular tickets instead of a pass for the journeys you'll be making. September isn't high season anymore and buying in advance will be quite cheap.

I'll do just a quick calculation for you :

From what I could see you live in the USA so 2 1st class Eurail passes would cost 1054$ (2×527) + the mandatory reservations. That's quite expensive !

On the other hand, regular tickets (bought way in advance) should be :

Paris - Lausanne TGV from 54€ (1st class)

Lausanne - Lucerne about 60 CHF for a specific connection (supersaver tickets) or 114 CHF for a ticket valid all day (1st class)

Lucerne - Zurich 30 CHF (supersaver) or 44 CHF flexible ticket (1st class)

Zurich - Milan Eurocity from 65€ (1st class)

Milan - Venice Frecciarossa from 30€ (1st)

This makes about 250 USD per person so half the price of the pass (and that's without reservations) !

For the day between Lausanne and Lucerne I'd recommend buying a 2nd class saver day pass (from 52 CHF) or a 1st class one (from 81 CHF) and that gives you a lot of flexibility !

It includes all trains, buses, trams, boats of the country !

For example you could take a train to Montreux, then the Golden Pass (panoramic train) to Interlaken, take a boat (included) between Interlaken and Brienz and a last train to Lucerne. It is totally doable in one day.

Let me know if you've got any other questions.