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EuroRail Help!! How much would it cost to book a reservation with my euro rail pass? Is the euro rail pass worth purchasing?

Hi! I'm coming from New York, US and am a little unfamiliar with the Euro rail pass but it seems like a pretty good deal considering I want to travel from Paris to London (over the course of 2 months). With that said, I want to know what is best for my money, also how the pass works.
Regarding the Youth 2nd class 10 day flexible pass to over about a dozen countries (valid for 2 months):

Can I visit one country which would take me about 4 hours (expected) and stay for however many days long I desire within that two month period and still have 9 days left to use?

Can I just find a train and hop on it to my desired destination with just my pass?

If I need a reservation which train lines require them?

Here is my desired route:
Paris to Geneva
Geneva to Milan
Milan to Venice
Venice to Rome
Rome to Athens
Athens to Budapest
Budapest to Prague
Prague to Copenhagen
Copenhagen to Amsterdam
Amsterdam to London

Out of those places which require reservations and how much do these usually go for?

Is it worth the extra money?

If I don't make a reservation and cannot find a seat can I still board the train and stand up?

And how exactly would I go about making a reservation with a euro rail pass?

I really appreciate your help!

Thanks a lot :)

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