1. Mostly no, most of the coins in these "Coins of all Nations" sets were not produced by the Franklin Mint. Franklin Mint were simply acting as a coin dealer, purchasing bulk foreign coins, "adding value" by packaging them up pretty, and selling them for a huge mark-up.
2. Yes, they used whatever coins they could obtain cheaply and in bulk. They are not "official sets" issued by the government that issued the coins.
3. Prices for Franklin Mint proof sets are generally better now than they used to be. The main thing you need to be aware of with these sets is that they can self-destruct, especially in hot, humid environments. While the quality of the coins in the sets is undoubtedly good, it's the packaging you need to be aware of. The pseudo-velvet which they used to line the insides of the proof set box emits corrosive by-products as it degrades. Red-dyed pseudo-velvet is the worst.
These coins were mass-marketed to non-coin-collectors. They usually came with a little instruction card on "how to care for your coins". The card told you to get some scissors, cut apart the blister-pack the coins were shipped in, put on the disposable gloves that were also shipped with the coins, and carefully place the coins into the pseudo-velvet-lined box.
This does mean that anybody who obeyed Franklin Mint's little instruction card - which would probably be a majority of the set's purchasers - inadvertently destroyed their coins. Ask any coin dealer who's had to handle a deceased estate of a Franklin Mint victim, a coin hoarder who bought thousands of dollars worth of FM proof sets and stored them away in an attic for several decades - it's heartbreaking to tell the heirs that all they have is a pile of corroded scrap metal. The only proof sets that are still in pristine condition are those that were stored in dry or cold climates, those who ignored Franklin Mint's instructions and kept their coins in the blister packs (which actually do a really good job at protecting the coins), and those which were bought by actual coin collectors who threw the packaging away and placed the coins in 2x2s or similarly protective housing.
The net result is that the surviving numbers of high-quality FM proof coins and sets is far, far below what the mintage figures might suggest. Reduced supply means higher prices for the survivors.
Don't say "infinitely" when you mean "very"; otherwise, you'll have no word left when you want to talk about something really infinite. - C. S. Lewis