Here's my opinion on these:
1a. I wish I would spend next weekend at home. NOT GOOD. It may technically be okay grammatically, but if so, it doesn't make sense logically. WOULD makes it sound like it is under the control of the speaker, so why can't he just do it--he doesn't have to wish. If you replace WOULD with COULD it would be fine.
1b. I wish I spent next weekend at home. INCORRECT I think you're using a past or present conditional to refer to the future.
1c. I wish I was spending next weekend at home. GOOD
1d. I wish I was going to spend next weekend at home. GOOD - same meaning as 1c.
2a. I wish he would own a car (now? or then?). NOT GREAT - I think this is technically grammatically correct, but it's rather unnatural. There may be rare circumstances where this sentence is appropriate, but generally 2b is much better and more natural.
2b. I wish he owned a car (now) . GOOD
2c. I wish he had owned a car (then). GOOD