Alfas have good brakes stock. A proper fluid flush, new semi metallic pads and new hoses should do wonders. It won't feel like a modern car but you should be able to lock up the tires.
Every time I have been driving my Alfa and get into our modern Mercedes my first brake application nearly puts me into the dash. Modern brakes are much more sensitive.
Regarding the second gear crunch, they all do that. Redline synthetic fluid (I forgot which variety, search on here) helps. But it's a design flaw they all have. Just part of the charm. Just shift into second slowly, and double clutch when downshifting and they'll go for years like that.
On my 73 Berlina the previous owner hot rodded it for racing and fast street driving. It was lowered, poly bushings in the wrong places, stiff springs, too much cam timing, etc. The closer to stock I get it the more I enjoy it. I do like the street Koni shocks, red I think. Yellow are too stiff for my taste. And as others have mentioned if you lower an Alfa too much the handling gets squirrely. Lots of people rave about the Alfaholics fast street package. Centerline springs are pretty stiff.
Lastly you can certainly run without a bumper, I have never had bumpers on my Berlina but plan to put the chrome ones on someday.