As someone who likes to have fun when I travel, am younger than most of the posters here (but not as young as you), and tries to eat/drink/stay on a budget, I'm going to give you my advice both for a radically different itinerary and budget tips for the cities you have chosen.
Keep Amsterdam, Berlin, but then head to Poland - I enjoyed Posnan as an overnight stop from Berlin but everyone I know who has been to Krakov LOVED it and it's cheap as dirt with fantastic cheap food. Prague is probably the most beautiful city I've been to in Germany and is cheaper than pretty much every city on your list as well. Keep Vienna, I always think of it as "affordable Paris" and feel it's underrated. Budapest has this amazing "crumbling glory" feel to it and again, is very cheap. Munich is a city that visitors love and all of Germany is surprisingly affordable. I don't want to tell you to cut Venice because it is astounding, perhaps make that your "splurge destination" but be aware of the crowds if you're going in high season. Then perhaps fly out of Rome. It would still be a pretty frantic trip and you could easily cut a couple destinations but you've got energy. Just don't forget how much transiting between places kills your travel days. Definitely look into budget airlines, if you're visiting places more than 6 hour train ride away it will almost always be cheaper and faster to fly rather than train.
I love London and Paris - they're two of my favorite cities - but for budget reasons I think you should cut them. London is just incredibly expensive, and Paris is for lodging.
Budget drinks and dining tips:
-London: Happy hours and pubs often offer specials for a "pint and a pie" - pub food in general. Food markets - like food trucks but with booths - are extremely trendy and offer amazing food for a good price. Borough Market is the famous one but there's small ones throughout the city.
-Paris: Bakeries! They often have savory fare such as sandwiches and quiches that are delicious and very affordable. They also sell soft drinks, so it's easy to carry your lunch to a nearby park. Or make lunch your main meal of the day and eat at a bistro with a set menu. Asian restaurants (ditto for London) can provide cheap, delicious food but check ratings on Yelp or Google because bad European-Asian food is pretty direly awful.
-Amsterdam: A lot of bars have a menu of things meant to be eaten while drinking, basically finger food. They're cheap and delicious, especially "bitterballen" (little croquettes served with mustard).
-Berlin and Vienna - A "butterbrezel" is a great snack/lunch at one of the uqitious bakeries, as are bakery sandwiches. Currywurst and Donerkepab and wurst stands in general will give you filling meals for under 6 euros. Berlin is the cheapest city on your current itinerary for drinking and eating, so if you wanna go on a crazy pub crawl, Berlin is a great city to do it in.
Venice - tiny bars called "bacari" (plural, "bacaro" singular) serve small, cheap glasses of wine and small bar snacks, usually sandwiches with cured meats or cheese and various deep fried things. Delicious and fun to hop from place to place and try a few. Sit down restaurants in Venice are generally pricey and not as good as other places in Italy, so don't bother.
Barcelona - Although tapas aren't native to Barcelona, there are tapas stands everywhere. Madrid is a better budget option because the tapas bars literally give you a lot of food for free when you buy a drink.
Keep in mind that while bars serving mixed drinks will be relatively expensive in most of these places, public alcohol consumption is allowed in most (check to be sure before you go). So buying a bottle of wine or a few beers from the store and say, sitting on the banks of the Seine at sunset is a budget experience that's hard to beat.