Please understand that 'I'll read a book' is NOT a future tense in this sentence. Many learners of English presume that 'will' is always a future tense. This is not the case at all. There are many different use of 'will' and and not all of them are to do with the future. In this context, it refers to a typical behaviour or habit in the present. It does not refer to future time. Yes, you can use a present tense, but the 'will' form is better. By the way, the 'would' form to indicate past habit - 'When I was a child I would often spend hours drawing pictures' - is the past form of this.

You can certainly use the present tense too, but it doesn't mean you can't use "will" as the original sentence does. "will" doesn't automatically mean the future tense. It can mean one's intention and yes, habits and tendencies too. "Boys will be boys" for example doesn't mean the future but that they tend to be, i.e, they habitually act like boys. On Dictionary.com, #7 meaning of "will" shows: "am (is, are, etc.) habitually disposed or inclined to:". So I say your example is fine as it is written. There are more than one ways to express the same idea.

Well done! Yes, you are exactly correct in using the present tense, because it is a habit. When speaking most English speakers might say: "I like to read books on my time off." It is very common to repeat the main verb from the question in your response, so in this case 'like' is the verb used.

I'm a former English teacher. My opinion: if you are talking about something you do alone ("I like to read books . . ") use the present tense. If you are talking about something you would be doing with someone else ("I would like to go to the movies . . .") use the future tense since it is something you may do that you are not doing now. Just my opinion. Bob