Determine the place value and total value of digits in given numbers, and form the largest and smallest numbers from given digits.

Here are the solutions to the problems:

1. In the number 228,320, there is no digit 9. Assuming the question intended to ask for the place value of the first digit 2:
The place value of the first digit 2 in 228,320 is the hundred thousands place.

2. To find the place value of digit 4 in 746,805:
The digits from right to left represent ones, tens, hundreds, thousands, ten thousands, hundred thousands.
The digit 4 is in the ten thousands place.

3. To find the total value of digit 6 in the number 694,529:
The digit 6 is in the hundred thousands place.
Total value $= 6 \times 100,000 = 600,000$.
The total value of digit 6 is $\boxed{600,000}$.

4. To find the total value of digit 9 in the number 9,634,567:
The digit 9 is in the millions place.
Total value $= 9 \times 1,000,000 = 9,000,000$.
The total value of digit 9 is $\boxed{9,000,000}$.

5. Given the number cards: $5, 6, 4, 7, 8, 9, 1$.

a) To form the largest number, arrange the digits in descending order:
$9, 8, 7, 6, 5, 4, 1$
The largest number is $\boxed{9,876,541}$.

b) To form the smallest number, arrange the digits in ascending order:
$1, 4, 5, 6, 7, 8, 9$
The smallest number is $\boxed{1,456,789}$.

c) Writing the numbers in words:
9,876,541: Nine million, eight hundred seventy-six thousand, five hundred forty-one.
1,456,789: One million, four hundred fifty-six thousand, seven hundred eighty-nine.

6. To write "seven million, seven hundred and seven thousand, seven hundred and seven" in symbols:
Seven million: 7,000,000
Seven hundred and seven thousand: 707,000
Seven hundred and seven: 707
Adding these values:

$$7,000,000 + 707,000 + 707 = 7,707,707$$

The number in symbols is $\boxed{7,707,707}$.

7. To arrange the following numbers in descending order (largest to smallest): $90,888, 91,888, 92,888, 93,888$.
Comparing the numbers:
93,888 is the largest.
92,888 is next.
91,888 is next.
90,888 is the smallest.
The numbers in descending order are $\boxed{93,888, 92,888, 91,888, 90,888}$.

8. To arrange the following numbers in ascending order (smallest to largest): $71,098, 16,009, 76,543, 54,112$.
Comparing the numbers:
16,009 is the smallest.
54,112 is next.
71,098 is next.
76,543 is the largest.
The numbers in ascending order are $\boxed{16,009, 54,112, 71,098, 76,543}$.

9. To round off 356,294 to the nearest thousand:
The thousands digit is 6.
The digit to its right (the hundreds digit) is 2.
Since 2 is less than 5, we round down. This means the thousands digit remains the same, and all digits to its right become 0.
356,294 rounded to the nearest thousand is $\boxed{356,000}$.

10. To find the square of 36:
The square of 36 is $36^2$.

$$36^2 = 36 \times 36$$ $$36 \times 36 = 1296$$

The square of 36 is $\boxed{1296}$.