I have 2 pony bottles that I use for solo diving, a 19cf and 30cf. I take the 19cf on the airplane, usually packed with valve off in the checked bag, although I have on occasion brought it on board in carry on when otherwise I'd be over the weight limit. Never had any issues with TSA.
When taking the 19cf to far away destinations I fill it at a dive shop or show up early at the dive charter location to fill it before we leave the dock (having confirmed beforehand that they will do it). Keep in mind it may need to have a VIP first.
On a recent trip to Truk lagoon given that the luggage capacity is limited on the puddle jumper flights, and there was a lot of switching planes and staying overnights during the trip, I secured a pony bottle on the liveaboard ahead of time so I wouldn't have to drag mine along. The attachment bracket is on my BCD tank strap so nothing extra was needed to secure the tank. I brought my pony reg.
As far as other gear for solo diving, I bring my own knife, backup shears, primary and backup lights, whistle, signal mirror, reel, dsmb, and Nautilus PLB. If I'll be penetrating wrecks I'll bring 2 reels.
I have only been prevented from solo diving in Greece and Australia as per the law in those countries.