CBR
Most of us on here who are current fz pilots are here to help, except Old King Coal he is here as the party Chief Whip.
For us to do that though you need to give us enough information to answer your question.
Re your medical limitation as an example, if your limitation is that you have one leg and therefore can only do crosswind landings and engine outs using left rudder the it is likely the GCAA will view this as an issue. On the other hand if your limitation is that you need to wear glasses for reading only then they likely won't care quite so much.
The others of you re start dates. This is how business is done here. If you can't take a joke, a wait or a poke in the eye with a sharp stick then don't join. Some people get interviewed and are sitting in a sim in Dubai 3 weeks later for some with the exact same experience, background and situation it takes 2 yrs. It depends on what list they pick up and when, what colour underwear they put on in the morning and if there is or isn't a picnic or route launch lunch that day with the invite sitting over your name in the list.
Do you really think that your start date is as important as that last nice looking bhajee?
The more luck you create for yourself the more you will have. Making your contact aware that you have nothing more important in your life, you are sitting with baited breath awaiting the aviation equivalent of the rapture so that you can transcend into the light and will be available at 30 mins notice to start will put you in a better postion than saying sorry I need more notice.
Though it is the case that most reasonable employers expect you to honour your commitments where you are as a demonstration of how you will conduct yourself here. This is definitively not the case here. Basically they don't care about what you do as long as you drop everything, trousers included for them when they ask, as often as they ask and do not expect the courteousy of the reach around or even the taxi fare home afterwards.