Could anyone please explain the usage of the future tense 'will' and 'to be +ing-form'? Is it correct to say 'I will clean the kitchen right now.' (I am about to do something in the very near future) and 'I am working tomorrow.' (my intention) Thank you very much in advance.
You sure can say "I will clean the kitchen right now." It sounds like a decision made at the moment of speaking. In other words, you didn't plan cleaning, but then you looked around and understood you couldn't put it off any longer, and said, "OK, I'll clean right now."
We use the Present Continuous to talk about the future if there are some arrangements (often with tonight, at 9, this weekend, etc.). So, if it's an arrangement, you can say "I'm working tomorrow." However, "I'm going to work tomorrow" may be better as long as you mean your intention.
Compare the Present Continuous (for arrangements) and to be going to do something (for intentions):
I'm having my hair cut today. I'm seeing my dentist tomorrow. I'm meeting Mike on Saturday. (I've made arrangements)
I'm going to get a job that earns me a lot of money. I'm not going to leave the house at all on Wednesday. (These are my plans)