Here are some examples of things happening now.

I'm just uploading some photos to Facebook and I'm sending a message to Billie.
We're all riding camels and the sun's shining.
They're waiting for me to get off the phone!

Yes, absolutely! You might not be having a driving lesson right at this moment, but it is temporary, so that's correct. We use the present continuous for longer situations like this too.

Yes, I’m glad you asked me that. We use the present continuous for future arrangements with other people.

At eight I’m meeting Lucas, just for a quick coffee.

For questions you just change round the subject and the verb to be. So, You are > Are you, then add the –ing form. Sometimes you need a question word first.

Are you working hard for the exam?
What are you doing?
Is anybody sitting here?

For negatives you add not after the verb to be. Don't forget to use a contraction if you're speaking.

You're not really studying at all, are you? (or You aren't really studying…)
They aren't using the computer room at the moment.
This program isn't working.

Yes, you're right. If a verb ends in e, you take off the e and add –ing

have - having          ride - riding

If a verb ends in a vowel + a consonant, the consonant is usually doubled before you add –ing.

swim - swimming           run - running

But be careful with verbs with more than two syllables where the stress isn't on the last syllable. With those you don't double the consonant.

visit - visiting          open - opening     

If the stress is on the last syllable, you do double the final consonant.

begin - beginning       

Whoops! Sorry, you can't say 'I'm understanding it'.

Yes, but there is a group of verbs which are called state verbs which we use for states (not actions) and we don't usually use these in the continuous form.

want - need - like - love - hate - prefer - believe - think - know - realise - understand - recognise - suppose - be - exist - appear - look - seem - belong - have (for possession) -  own - feel - smell - taste

Yes, excellent.

Yes, they are correct. But the meaning of think there is 'having thoughts in your mind' or 'considering'. It's not the same as 'having an opinion' about something.

I think that song's brilliant.   (opinion)
She's thinking about studying archaeology.  (considering / wondering about)

No, sorry, that's not an exception, that's wrong!

Well, OK, maybe it's a new usage. English does change. But don't use it in exams!