There are no hard and fast rules about Modern Art, as so much depends on the mentality of the fellow players. However, general rules of psychology, bidding games, and trading can help.
To start with consider these things:
1) The threat of being out-bid is more powerful than outbidding someone. This means you always want to have more money than your fellow players. Too often newer players will buy up paintings that will score early, then allow the remaining players to get the same artists at lower prices (since they're out of money). Try playing with losing every auction first round, to see how it feels to be really rich. With this strategy, you'll want to end round one as quickly as possible.
2) Don't overpay. It sounds simple, but there's an opportunity cost (to buy something else) whenever you buy something. Here's some math to estimate prices. In an optimal game, every round consists of 3 artists only in proportions of 5/4/4 (=13) with an aggregate 'price' of 5*30 + 4*20 + 4*10 = 270 / 13 = ~20. This means all things equal, don't pay more than 20 for a card, first round.
3) Keep track of # of remaining artist cards! This is a game of psychology. It's important to know what your opponents are likely to have in the their hand. Likewise, keep track of your opponent's play styles over rounds or multiple games.
4) Tips on auctions:
- In Free Auctions, psychology tells us that players tend to overbid. This is due to 'loss aversion' and the mistaken belief that you're denying an opponent something he wants. Try to bid up your opponent, if you have the guts, to make him outbid you and pay too much.
- In one-round auctions, you have the advantage as the auctioneer if and only if you have a big pile of cash (see #1 above). If the last player bids too high, let him have it, else take it for yourself.
- In secret auctions, players are trying to read each other, and tend to overbid because they think that adding 'just a few extra' will win them the auction. Try lowballing these auctions just in case someone gives up with nothing (bidding nothing is a terrible idea)
- The fixed price auction is your best opportunity to play strategically. Only play one of these when you know an opponent will overpay. No one will let you buy it too low, so never offer these under-value (unless you have ALL the money).
- The dual auctions are wonderful ways to grab art. Try using it only late in the round with the one-round auction. If you have a pile of cash no doubt this is an opportunity to get a lot cheap, or get a pile of money for next round.
To answer your specific bullet points:
- As for which artist to play, you want to 'team-up' with a specific other player. A win for you and one other player means a relative gain against two other players (assuming a 4 player game). Concurrently, this means that you play cards already in play and hoard artists that haven't been seen yet (they will later).
- The artist tie-break is game balance, but doesn't quite fully balance things. The artists with the more cards are therefore slightly more valuable.
- Play most auctions to well-below value, and play the one-rounds to win as auctioneer.
- Doubles are more powerful later in the rounds, but only if you have a cash advantage.
- 4 rounds * 3 winners per round / 5 artists = 2.4 So, each artist, on average places 2-3 times a game. That's quite significant. Keep track of the artist and place: if the 12-card artist places first, forget about him scoring the rest of the game, but if the 16-card artist places 2nd or 3rd, that's a good bet to try to win in subsequent rounds.
Hope that helps!