#1: N, then T, V, W, X, Y, Z the next letters of the alphabet composed solely of straight lines.
#2: Count the number of letters in each number-name: ten, nine, sixty, ninety, seventy, sixty-six. Each one is one letter longer than the previous one and is the largest number of all numbers spelled with that many letters. Since 66 has eight letters, the next in the series must be the largest nine-letter number name. A common answer is “ninety-six”, but the biggest one is “ten googol.” A googol is 10 to the 100th power (i.e. 1 with 100 zeroes after it). The hint was in the source of the question. Google got its name from the number.
#3: 20; positive integers that start in English with the letter T, written in ascending order.