Almost done planning, what do you think?

If you split the car rental price four ways, it won't be that much. Although as Tony mentioned, you'd need something of decent size. Have you checked prices - googled for it?
Tony is the expert as far as t schedules and public transport are concerned - I simply have to admit I do not know have any bright ideas how to solve your problem.

Jerez can get busy, especially cheaper places. I'd book.

cheap accommodation Jerez

Click to enlarge, tell me if you can read it, it's been scanned.

Tarrita

Q1. I'm not sure why you're reluctant to take a taxi. If it's on the grounds of cost, I can understand that but you have no other choice at that time of the morning. If on the grounds of safety, I would think that you're going to be fine. I've never heard of any solo woman coming to harm in a Madrid taxi. Otherwise, do a Google search for "transfer barajas madrid" or "transfer airport madrid": you'll get some results that might be interesting.

Q2. I gave you all the public transport details, including times and options, on how to get from Jerez airport to Jerez, Cadiz and Conil on one of your other threads. I'm afraid you'll have to go back and find them. (This is why it's best to stick to one thread - flitting about from thread to thread, looking for stuff already posted gets tiresome. Do a search under your own name - top of this page.) However, it looks as if you've decided to stay the night in Jerez. If your flight gets in on time, I think it would be a pity to wait around at the airport till 1830 just to save a few euros. Get a taxi into Jerez if you can afford it.

Just in case OP looks in - there are no flamenco concerts on Thursdays this year in Cadiz (referring to Chanol's post) - they're on Fridays, which has just been confirmed by the tourist office today. That's one of the problems I find with flamenco establishments in Cadiz - the penas do not confirm their program till the last moment. I did not comment as I did not have the info till yesterday.

Last year Jueves Flamencos did not start till 15th of July... The best way to do this is to confirm "agenda cultural" at the tourist office as you arrive. There are "actuaciones flamencas" in Jerez this Tuesday, but, if you look in, Tarrita, and you have decided to spend the 11th in Jerez, please get info at the tourist office as I do not want to be responsible for any possible misinformation. I went to a flamenco gathering yesterday - it was supposed to be in a Pena in El Puerto. After having arrived there, I found a hand written note: We have moved to Hotel Monasterio. Such things simply happen... The tablao " la Cava" in Cadiz does shows on Tuesdays and Thursdays - 20 euros for "entrada" and 1 drink.....

Hey NavajoRub, are you sure about the friday flamenco thing in cadiz? It wouldn't be the first time that you get different answers with regards to all things flamenco around here, but I heard that Antonio el Pipa is performing in that concert series on the 19th (thursday) at the Baluarte....this source came from El Pipa's guitarist who is a friend of mine.....

The website "deflamenco" has a fairly complete (but not everything) list of flamenco happening all over Spain and beyond...check under "agenda". And for those in the area, don't miss the first annual "fiesta" dedicated to the memory of Luis de la Pica.....It's going to be the WWF of flamenco events!

Hey, Chanol. I asked three times and was told Friday but I wouldn't be surprised if it turned out wrong. As you say, the usual uncertainty. Seems like you've got info straight from the horses mouth though (so to speak). If I am off work, I am going to the Luis de la Pica event. Also, El Cigala is playing in Puerto on the 17th - I actually sort of like him (shhh). Tickets are 30 euros though.

There are summer concerts at the Catalina castle in the evening but only a couple of them are flamenco related - the posters are plastered all over Cadiz. There is also a festival of international music, so one wouldn't be bored.