I would take off the gyro and grind the tabs down just so it looks better and cleaner (I hate gyro tabs). And taking down the front brake tabs would be fine too. You can also grind down any extra bits of axle sticking out past the nut. I do it on my rear wheel to save from any axle to ankle slips. Just be very careful with the grinding wheel - mark out first with a Sharpie then take off a little by a little.
Grips are fine and don't mess with that front axle washer - it looks like it might be a convertor from 14mm drops to 3/8" axle as well.
I'd go a pivotal seat/seatpost. There are a ton of them out there. Depending on what your current setup is you could save a bunch of weight there.
From the pics - the tires look like they could use an update. Folding are $$$ but will be light. Cheaper option - just go for normal wieght tubes and resonable weight tires and get a good tread to match what you ride most. Also spend a few bucks and get a good rim tape - I like Velox. The stock Haro rubber ones are probably pretty shot. Good tape will help with flats.
Like others have said Nation and Staff will have a great selection. If Effinger's is close tho go there - they looked to have a solid BMX selection when I was in there a few months ago.
Here is a good thread on 20" stuff:
http://www.ridemonkey.com/forums/showthread.php?t=202461
Also check out
http://bikeguide.org/ and
http://www.bmx-forum.com/
Show some pics when you are done with it.