First buy to let offer accepted- what’s next?

Finally I have managed to secure a property as my first buy to let. I had posted previous discussions which have helped me in making an informed decision. As I have now my offer accepted, I have to send my solicitor details and start with all the formalities. But before I could dive in this process, I have couple of queries.

1) I bought a property for 310K, and putting down deposit of 124K (40%), any tentative figure you can advise that will be added to this deposit. Do you think 10k will be enough to put aside including stamp duty.

2) I am going for second viewing tomorrow so I am wondering what things I should check for in property to make sure they are fit for prospective tenants per legal obligations. Currently owners are living in there, so when I first viewed the property it looked Ok on kitchen and bathroom. Boiler seems to be old, so might need replacing but If the owner is living in that house it will be working and should be good for tenants ? or if there are any legal obligations to have new heating system in place. Anything other than heating you think I should check.

3) Any idea on how much a solicitor fees will be ? and do I need to find solicitors which are expert in BTL ?

Many thanks

Kaps