Assuming that the four-sided spinner is fair and that it is numbered in the traditional way of 1, 2, 3 and 4, the probability of spinning a three is 1/4.
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Presuming that the spinner and the number cube are both "fair", then no - spinning the spinner and tossing the six-sided number cube are called statistically independent events. They do not influence each other, and it does not matter which order the events occur in.
If there are four colors on a spinner, then the probability of spinning one particular color is 1 in 4, or 0.25. Also, the probability of spinning one of two particular colors is 2 in 4, or 0.5. Combining these two "unrelated" events simply requires multiplication. The probability, then, of spinning one particular color on one spin, and then spinning one of two particular colors on the next spin is (1 in 4) times (2 in 4), or 2 in 16, or 0.125.
Assuming that by " a club", you mean as in a deck of cards. Without jokers, 1 in four.
The probability of rolling a four on a 6-sided die is 1 in 6, or approximately 16.67%. Since the die has 6 equally likely outcomes (the numbers 1 to 6), and only one of those outcomes is a four, the probability is 1/6.
It depends on the numbers on the 4 sided die. I don't believe that is a recognised standard.