I have recently completed the process for applying to join as an AET.
Questions you will be asked are not really service specific. They want to know what your interests and hobbies, how does your family think or feel about you applying, financial commitments, do you understand some basic information such as where is basic training, how long for, what is your minimum term etc etc.
I would wear a full suit - as others have said.
For running I followed the 8 week pre fitness course. I ran a 2.4km run in about 15/20 minutes.
Follow the plan and your run will naturally decrease. Also add some interval training in - that has helped me go from 11:30 to 11:12 recently (I am trying to get my tun to sub 11 minutes...my pass time is 11:58 for my age)
Personally I would mention the cadets (they will ask you if you have been a member of any uniformed cadet service or group).
Swimming - like your running you simply have to get it done. Speak to the leisure centre and see if they have an instructor who can assist. When I joined up at 16 we had a lass who turned up and couldn't swim. PTI's got her through it the "Navy" way which as you can imagine wasn't the best.
The only thing you control is how fit you are prior joining! The rest they will teach you or you will learn.
Fitter you are - the less stressful your time will be during basic. No PT remedial stuff means more time for kit