I have a Daiwa BG 20 would this reel handled big reds and what ever else I catch on the pier or jetties. And can it be spooled with braid?

A bull red will be pushing the limits of that reel. Maybe over the limit. That is a perfect reel for fishing the surf or the bay. But if you are wanting to drop 6” mullet off the end of the pier targeting bull reds or sharks then you should go big.

I love that reel. I have the 30 and 40 version of that reel. I use them for kayak fishing and have caught everything from bull reds, shark and countless kingfish.

The big difference kayak fishing is im not locked in to a spot. I am Mobley so line cap isn't a big issue

I have a small fleet of BG's 3000-6500's and I love them all.For your purpose I'd go with a 4000, it'll hold 250ish yards of 30 lb braid which should be plenty to keep you from getting spooled.You could go with the 3500,the only difference between the 3500(a little over 200 yds of 30 lb braid)and 4000 is spool capacity and maybe a half oz.I'd go for the spool capacity but that's just me.

do they come left handed?

The handle on the Daiwa BG spinning reels is interchangeable from left to right and back again.