Oui

It is a must to do both. I bought an English guided group tour. There are tours that are 3 hours long and I have seen one that is advertised as ‘Tour of Alcázar with an official guide Tour of Seville Cathedral with an official guide’. I would suggest as you have only three hours to see the Alcazar first and the cathedral after as there is time taken up to climb the tower which in your case with time a problem, is not necessary and could be cut out if it is at the end of the tour. However, if you go with no guide you can make it as long as you wish. The gardens of the Alcazar are pretty but personally I thought the architecture is stunning and with a guide to explain, was well worth the time and money

EU citizens only. We were there this week, I asked in advance and was advised as we were UK citizens we had to pay full price. We had to supply passport details to book online tickets too. Just one more negative outcome of Brexit

I would doubt it, they only have a limited number and they sell out quickly.

There was a QR code on the arrival which opens an audio guide. This was free. You need something to get a proper information and feel of the place. I found the guide little bit difficult to use, you had to choose the place or room instead of it going in order, but you will used to it. ( you might miss the QR guide if you don’t look carefully, it is not very obvious) Worth visiting! Enjoy.

Hi. We booked our tickets at the Real Alcazar de Sevilla Web site.

Yes you can but it must be booked well in advance on their website to trigger it for 1 euro each (booking fee)

They sell out pretty fast for the Kings Rooms. Hopefully you can get tickets to the grounds and palace. It's a beautiful place.