Was Willoughby lying:-

1. About being drunk?
I don't believe so. Everything he says about the timing of his journey and his brief stop at Marlborough makes perfect sense. The fact that Elinor is convinced that he isn't intoxicated by "the steadiness of his manner, and the intelligence of his eye as he spoke" confirms the matter for me. It was a hard-drinking age and I'm very sure that Elinor had seen the effects of alcohol often enough to recognise that it isn't alcohol which is responsible for his manner.
I read his "Yes, I am very drunk.." line as irony - not a joke as such, but a sort of verbal embellishment which he is hardly aware of. My sense of Willoughby here is that he is not drunk but is very wound up, partly because he must realise at some level that he ought not to be at Cleveland at all.
Though I do not think W was drunk, I reckon that after he left Clevedon he stopped off at an inn to drown his sorrows and got absolutely blotto. I expect he had a hangover the next day, and serve him right!

2. Did Willoughby not know Eliza would be “reduced to the extremist indigence” after he left her on her own?
If he had thought about it he probably would realise that she might be so 'reduced', but I rather doubt that he thought about it at all. His treatment of 'respectable' women like Marianne and Sophia is so unfeeling that I would not be surprised if he bought into the widespread misogynistic attitude that a woman who surrendered her virtue merited no consideration whatsoever.

3. Did Willoughby forget to give Eliza his address?
It probably didn't occur to him to do so. After having his fun with Eliza and beginning to be bored, some more alluring opportunity arises, such as an invitation to visit friends, or the chance of pursuing a £50,000 heiress. So off goes Willoughby; he tells Eliza he'll be back (and it's quite possible that he will be - he hasn't thought that far ahead), so he has no particular reason to leave her his address.

4. Does Willoughby really not remember if he told Marianne he would return to Barton?
That last conversation with Marianne must have been pretty fraught. I think Willoughby probably fudged the issue of when/whether he would be back. He could not possibly 'confess all' and tell Marianne the truth about why he was leaving and could not return to Barton. He may also have had it in mind that if his plan to marry Sophia failed, something might turn up which would enable him to get back with Marianne.
So W probably did not deliver a clear message, and very likely didn't remember exactly what he said.

5. Did Sophia compose the dreadful letter Marianne received from Willoughby?
Yes and no. Here's how I imagine that conversation with Sophia:
I agree with Amytat that W must have tried to convince Sophia that he was just friends with the Dashwood family etc. So Sophia says he must write to Marianne and return the letters. Willoughby says that he'll do it today, but Sophia insists that he does it right now or the wedding is off! W hesitates or can't find suitable words, but S says something along the lines of "You've just explained it all to me. Where's the problem? Oh, let me do it." She drafts the letter, reflecting what Willoughby has just told her, and he can either copy it out and send it, or wave goodbye to £50,000.