I actually think the whole set up isn't fair, his expenses are fixed, where as yours are variable, dependant on how both of you decide to live and subject to short notice change.
A much more reasonable arrangement would be to set up a joint account just for rent and bills, you both pay into that, and while his contribution should cover rent and yours bills, if the bills increase you are both responsible for finding the difference. It will allow you to plan (I'd aim to pay a little more in each month than you think you'll need too, that way you've got a bit of a cushion for big bills, eg. electricity and gas over cold winters compared to summer costs) and make him aware of what the true costs are, not just defaulting to you.
As for the rent and deposit split, you don't have the money, make it clear you don't have savings (FYI, you really need to start getting some of those) and why should you ask your dad?
Be warned, if you can't afford this place on your own but he can, if you split up, I would assume you would move out and he would keep it on, that would mean you'll find it very hard to get this deposit money back until he left.
Also, under your current (slightly odd) arrangement, if he's responsible for the rent, why on earth would the first month's rent be any different to the second months rent?
Realistically, you might need to accept you can't actually afford to move in together right now if he expects you to pay 50/50 like a flat share, in which case he can either get the flat on his own until you're able to move in, or you will have to continue to live separately until your income increases.