If the G20 nations (or most of them) ban bitcoins doesn't this effectively kill bitcoin? My thinking is that a normal person would no longer have any means of converting bitcoins to the local currency. The only other way this would work, were if most places took bitcoin (coffee shops, grocery stores), but if it's banned then most of the places would stop taking it.
My thinking is that (i) G20 nations are democracies, and (ii) Bitcoin is a useful service. If it's useful to people, and people want it, they'll vote for it and it won't get banned.
If your country bans something useful to the masses, it's not a democracy. It will be banned only because it lost its utility, and if that happens, there will probably be something better replacing it.
1- Pretty much
2- Yes, all trasactions are public. You can use websites like blockchain.info to see all the transactions happening. And yes the US government is starting to do do things like this: https://www.fbo.gov/?s=opportunity&mode=form&id=15d43de53e969bd779d48252d69c1307&tab=core&_cview=0
No need to apologize for your question! We're all here to learn. For every question asked, there are many lurkers wondering similar things.
Some food for thought on point 1:
Illegal drugs are already banned in most places; did these commodities become more or less valuable after such bans? There is a good discussion between Stefan Molyneux and a caller to FreeDomainRadio here: https://www.youtube.com/watch?v=G6UVQUjS1T8 (warning - video has a not-safe-for-work title but the content is audio-only and is not offensive)
Since bitcoin itself is a currency, as infrastructure and networks and cryptoeconomies evolve, shouldn't the need for conversion into fiat diminish anyway?
The question really hinges on timelines. In the short term, large bans would have an effect but they would also create competitive opportunities for other countries. Lots of venture capital is flowing into cryptocurrency right now. Governments all want a taste of that, so they are necessarily hesitant to use the ban hammer.
 Bitcoin works because of Satoshi's foundational discovery/contribution/invention in computer science that allows for a distributed, decentralized, public ledger. All transactions are publicly visible but to tie a transaction to a person, you must also tie an address to a person. The entry for a transaction in the blockchain will show bitcoin addresses but not your name or other identifying information. If someone looks at your computer and sees that you control a certain address, they can then do some blockchain forensics to see with whom you have been transacting. Interestingly, it is trivial to create a new address for every transaction and many services do this automatically. Additionally, services like CoinJoin obscure ownership by 'mixing' coins. Projects like Dark Wallet are working on integrating this sort of coin mixing into normal wallet operations.