First of all who is the house builder? You really need to name and shame as a warning to others.
I am not sure why you are using an estate agent to deal with the builder regarding your defects and snagging.
You should always write a letter to the house builder listing what is wrong and what needs doing.
For sure, you shouldn't be doing your own snagging to reduce the number of items.
What incentive will any house builder have if they realise buyers are prepared to do minor snagging themselves?
Painters all over the country will leave the undersides of window boards knowing there will be no comeback. They save a little time and they still get the same money for painting the house!
Without doubt you should insist on a new cooker as cracks are unacceptable as would a repair be.
Cracked wall tiling should also be taken off and replaced and anything else that you are not happy with!
You would have been better to have used a professional snagging inspector before you moved in, then the builder would have had to fix everything before you bought the home. failing that, the
extensive snagging lists and the information and advice on this website would have been of huge benefit to you.
What to do now: you must WRITE to the house builder/developer giving them a deadline to attend to the items in the letter. If they don't, make a claim under your NHBC warranty - which can be a long and tedious process with no guarantee of a successful outcome.
You really must take charge of this yourself, not leave it to third parties.