Your employer should have a parental pay and leave policy. Check your contract, employee handbook or other relevant documents.
Your employer might offer enhanced (contractual) maternity pay, but if they don't, the minimum you will get is Statutory Maternity Pay (SMP) which is 90% of your salary for the first 6 weeks and then £156.66/week for another 33 weeks after that. If you want to take more than 39 weeks maternity leave, the rest would be unpaid. Alternatively, you could end your maternity leave but use some annual leave (that is accrued during maternity leave) to get full pay while extending your time with baby a bit.
Most people can claim child benefit - you will need to register the birth first, and you have up to 3 months to claim (not 6 weeks as a PP said). It can be backdated to the date of baby's birth.
As for whether or not you will be entitled to other benefits, this depends on your circumstances. You might be able to get some Universal Credit - this depends if you have a partner, how much you (both) earn, whether you (both) have any savings, whether you rent, and other factors.
If and when you return to work, you may be able to get help with childcare costs through Universal Credit (if eligible), but if not you are likely to be eligible for Tax Free Childcare instead.
And yes once your child turns 3 - well, the term after they do - you should get 30 hours a week funded childcare (term time only). You need to be working to qualify. If the child has a SAHP they would only get 15 hours a week.