Point 1 of 'Things for you to do' in Lesson 4 is discussed in Lesson 9.
For Point 2 - here are my thoughts. I am not sure if they are correct. Please correct my mistakes.
Different base systems that we use in daily life - We seem to be using many base systems, in the sense, our counting goes back to zero once the highest number in the base is reached. But still to count up to the highest number, we seem to be using decimal system only. So, I am not sure if we can treat them as a different base system. Here are a few examples -
a) Base 2, base 8 and base 16 are used in computers. They do not use the decimal system. They are called binary, octal and hexadecimal system respectively. They represent the bits and bytes of the computer world.
b) Base 7 or rather counting up to 7 and reverting to zero is used in week calculation. We say there are 7 days a week and the 8th day becomes the first day of next week. This seems to be using the decimal system.
c) Base 12 uses counting up to 12 and starting back from zero. This is what we call a dozen. Also, an hour is divided into 12 five minute slots and a day is divided into two 12 hour slots. A clock has numbers up to 12. Also in astrology, the whole space is divided into 12 houses and the planets are placed within these. A year is divide in to 12 months.
d) 30 is used for a month. Each month is roughly 30 days.
e) 60 is used to represent number of minutes in an hour and number of seconds in a minute. For any calculation of time, we need to be familiar with 60 and its fractions and multiples.
f) 360 is used very commonly in geometry. A circle is divided into 360 degrees.
however, except base 2, base 8 and base 16 we seem to be taking the help of decimal system for the other bases.
It is believed that base 12, base 60, base 360 etc were used by different civilizations. On searching the internet, we find many civilizations claim to have discovered the place value system.
Anyway, the decimal system, which we believe is the contribution of Indians, is widely used today. This could be because the presence of zero simplifies calculations with large number of digits, especially multiplication and division. We have ten fingers on our hands and counting with fingers probably made humans to adapt to decimal system. However, decimal systems simplifies the various mathematical operations that it is hard to imagine maths without this system.