Yep, I imagine that the reason for April is because the initial 2 year fixed period on their current mortgage ends. So if you step in then, you avoid paying the extra early break fees that you’d be liable for if you were to do it now.
I think in terms of costs, you’ll have to pay a solicitor to transfer the brothers share to you. And then work out what the cost is to buy him out based on current value, the deposit he paid, and the fact he’s been paying mortgage for 2 years.
There will then be a cost to set up a new mortgage with your name on it, but that will probably feed into your monthly payments, so not be a one off payment in April.