The Future Continuous Tense

Hello, guys! Can I use the future continuous tense in this case, "In the evening we won't be watching TV, we will be reading a new book." or It should it be expressed with a help of by or with the future simple tense?

Your sentence is absolutely correct in American English. Other examples are:

1. We won't be studying German tomorrow; we will be studying Italian.

2. We won't be going to the beach tomorrow; we will be going to his friend's party.

3. We won't be making spaghetti tomorrow; we will be making lasagne.

Here is a similar grammar pattern used in American which essentially means the same thing.

1. Instead of studying German tomorrow, we will be studying Italian.

2. Instead of going to the beach tomorrow, we will be going to his friend's party.

3. Instead of making spaghetti tomorrow, we will be making lasagne.

the future continuous tense

Hello, guys! Can I use the future continuous tense in this case "In the evening we won't be watching TV, we will be reading a new book." or It should be expressed with a help of the future simple tense?

The future continuous tense is fine here Maks.