I used to play M:tG quite a bit. Haven't played more than a game occassionally, here and there, in a few years now. I've played in a few tournaments, and done fairly well sometimes. But my favorite games were the friendly games -- just folks playing to have fun.
Since most folks above are answering on the assumption of tournament games, I'll answer from the point of view of friendly games:
How long do games last? Is there a time limit?
No time limit. Play until someone wins or you get bored. Most, average games take anywhere from 15 - 60 minutes.
I used to have a 500-card deck that had 4 of every healing or damage-prevention card printed. It had no way to directly win; it was all defense. It drove more players crazy trying to beat me than any other deck I ever built. Guys with killer decks (of ~60 cards) would get really mad when they couldn't kill me in 10 minutes. An hour would go by, then another hour. One game went on for over 5 hours, no lie, before my opponent gave up (and I still had a few hundred cards in my deck). All my victories with that deck (maybe 50% of my games) came from the opponent conceding the game.
How are the cards randomized? How do you keep somebody from manipulating the order of the cards?
Shuffle the cards just like a normal deck of playing cards. Cheating is cheating. You deal with cheaters the same way you do in poker: shoot the offender. I only had to do this twice. (Afterall, I usually played with friends
Are the cards in one player's deck kept secret from the opponent?
Like an RPG character sheet. Some are mortified if you saw their deck contents, some didn't care.
If you have only one deck, the folks you play against figure it out after you play them a few times. But many people were always tweaking their deck, so they always evolve over time. Most people had more than one deck, anyway. There were many times when players completely show one another their deck. Among friends, deck contents were not state secrets.
Maybe I missed this, but are silver and gold cards (uncommon/rare) more powerful? Is there a limit on the number of silver and gold cards in a deck, percentage-wise? How do you "maintain balance?" Could I have a deck made up only of rares?
Rarer cards were not really "more powerful", but often they had more interesting twists. Just like in D&D: a 5th-level human fighter is CR5 (common); a troll is also CR 5 (uncommon); a young black dragon is also CR5 (rare).
A rare card by itself is not a game winner. I've seen whole decks of rare cards loose to a deck of all commons. There was nothing inherently powerful about a rare card. For instance, you could have a bunch of weak common white creatures in your deck (weak usually also means easy to get into play quickly), and then have a rare "boost all white creatures" card to make them all better.
One of my fellow players in my D&D group bought 4 special decks from Origens last year. They are prebuilt decks, with special backs (not legal for tournament play), but we played them against each other for several games and had fun.
Also, you can play multiplayer Magic, as well. I used to love having 4-6 players. It opens up all kinds of different strategies, and those fast killer decks that everyone plays at tournaments don't work so well in a multiplayer game.
Bullgrit