Very good questions. I'm sure everyone is different, however, my experience with two boys 2 1/2 years apart is great.
While I was "big pregnant" my little guy would say, "Go away, Mommy... I'm playing." Cool! He was getting into the phase of independent play and wanted to explore his toys on his own. That just meant I didn't need to engage him all the time. I would lay down on the couch and rest for a while. It worked out just fine for me. ;)
As far as keeping quiet... I never got wound up about this one. I figured there was going to be noise and the baby would have to sleep anyway, and guess what? The baby slept through any noise the toddler came up with. Of course, I did try a little to keep things to a dull roar, but I think babies and children in general have a different way of dealing with that... which brings me to your last question... My older boy was never bothered by the baby's crying. They did sleep in different rooms, but it never woke him up. I was shocked sometimes, but he did just fine.
The tantrum throwing is going to happen. What I did to minimize that is to involve the older one in my activities with the baby. I don't know if he understood anything, but I explained everything... just talked as I did whatever I needed to do... explained what I was doing and let him help as was age appropriate. If he didn't want to help, that's fine, too... asking is important... involvement is important. I also let him snuggle right up and watch a movie with me while I was nursing/feeding the baby. He's not going to hurt anything by snuggling up to the baby and you can explain the process that the baby gets milk this way... "isn't that so cool!?"
Have snacks handy - like right next to you in a little canvas bag - ready to give to the toddler. I had a chair set up in the living room that was my "space station" with everything I could think of that I might need right nearby. Including diapers for both the baby and the toddler. It wasn't pretty, but with cute baskets or bags, it didn't look like the mess it could have, either. Make it easy on yourself and don't worry too much.
Going out with two takes a lot more time to get going, but wasn't really a problem for me. I took them everywhere. Grocery shopping, hair salon, church, everywhere. If you let them understand what's expected of them and give them a chance to experience the process/activity, they have a better chance of behaving properly.
My guys are now 6 1/2 and 4. Happily adjusted, great kids. Don't get me wrong, though... lots of frustrations and bumps along the way, but with a little patience and love, it all works out. They fight and scratch, but they also play and love each other dearly.
Best of luck. Children are wonderful. :)