I don't think other altcoins affected the price of bitcoin in anyway, even if the altcoin claims that they are some kind of improve "bitcoin" even on launch of ICO, bitcoin prices are not affected. Also other altcoins have failed to overtake bitcoin they can't even go near the price of bitcoin. But I guessed when all the altcoins are non-existent maybe Bitcoin price will go up as their will be no altcoin trading that will happen.
Because of the altcoin promoters online, more people have become aware of crypto-currency. Even if it's not directly bitcoin that they are promoting, it still affects bitcoin since it's the primary crypto-currency out there.
Yes, altcoins are far cheaper than bitcoins. It's because there's a huge difference between the amount of people that invest in bitcoins and people that invest in altcoins.
As for the price, there are altcoins out there that are really expensive and I think there might even some altcoins that have a higher price than bitcoin itself but all of them are dead coins. The price of the altcoin doesn't always symbolizes success. Sometimes they just put a high price on it.