I hate being asked how toI spend my day off.

I have nothing to do on my day off, but most people say it's waste of time.

Having a good rest at home on my day off is not bad thing, isn't it?

I hate being asked how toI spend my day off.

I have nothing to do on my day off, but most people say it's waste of time.

Having good rest at home on your day off is not a bad thing, isn't iright?

I hate being asked how toI spend my day off.

"How to spend" means others are asking you for tips on what to do. "How I spend" is what you're going to do.

I havedo nothing to do onon my day off, but most people say ithat's a waste of time.

Having nothing to do implies you're bored or don't know what to do on your day off. By the sound of it you're deliberately doing nothing, so you'd say "I do nothing".
"That" is used to refer to the previously mentioned act of doing nothing.

Having good rest at home on day off is not bad thing, isn't it?

I hate being asked how toI am spending my day off.

It sounds better when you use 'I' and the present progressive tense here. What action is ongoing during a specific period of time.

I have nothing to do ondon't do anything on my day off, but most people say ithat's waste ofing my time.

You have nothing to do sounds like you have no jobs or tasks you could do which may be true but it sounds more natural to say 'I don't do anything' which makes it your choice. I would say I would use the present progressive tense is better again an ongoing action during a specific period of time.

Having a good rest at home on a day off is not bad thing, isn't it?

You need the indefinite article before 'good rest' and 'day off' to introduce them. Tag questions in English are usually, although not always, negative if the main verb phrase is positive and positive if the main verb phrase is negative. So 'is not a bad thing' has a tag question of 'is it?'.