1, Leasehold is definately ok…I m in the process of buying two properties in London at the moment, they both are leasehold…The only problem you might have is that the deal will take longer than freehold house to complete, because your solicitor will have to contact the land owner who is well known for taking time replying…
2, Once you agree the price with Vendor, if you pay 100% by cash, then you can almost do it straight away. Inform your solicitor and get the deal done. The solicitor will do all the paperwork & valuation which will take approx 4 weeks, they will set up the exchange date which is the date you exchange contract and pay deposit(usually 10%), then followed by completion date which you obviously will pay the rest of the money then get the key… if you need a mortgage, then its a little complicated, you will have to agree with your building society how much they can lend you, they will also send the valuator to your property to make sure its worth what its selling for…
3, regarding to the timing, I would say its much depending on yourself. If you buy it for live, then it probably doesnt matter when you buy…but if you buy it to let, its a different matter.
Anymore questions, you can pm me, I might not be able to answer all of them but I have some very good contact that will for sure be able to assist you.