You can download a really helpful guide to the party wall act here.
www.communities.gov.uk/publications/planningandbuilding/partywall
I woud recommend reading this 1st, it also has sample notice letters in it.
As a professional who deals with this kind of thing all the time I'd get the party wall sorted out asap - you must get this addressed prior to starting work and it can hold up anything if there are issues
Your drain issue will probably not be covered by either of these unless you are doing specific improvement works to it - you may need to get a new agreement to cover this issue. A surveyor may be able to advise you of how to approch this.
As a householder you can probably get free advice on how your local buidling regulations officer would like you to proceed and the extent of the information they require from you & inpections etc. Some parts of the buidling regulations can be self certified (fensa window scheme, electricians etc) others will require inspections. See your local council's development control webpage for more details and have a chat with them they are usually quite helpful.
Who has being doing your drawings? If its an architect then they should be advising you on this and all the stages. If you have just gone down the plan drawer/ draftsmen route then you may have more difficulties with the next stages as you are effectively going to have to manage the whole process yourself and you have no guarentee they know what they are doing past picking up a pen.
Don't panic, just be logical and plan out what needs doing. Some contractors will sort out building regulations drawings for you, some draftspeople. Be fastidious about checking them - is a new kitchen going in as part of the build, who is designing and fitting this. the contractor or a nominated subcontractor. What do you want included or excluded in the build - is it a shell or is it to be finished to the final detail or somewhere in between.
You can put out to tender on Planning drawings with a written specification ( I would write a performance specification - what it needs to do - meet building regs/ any planning conditions etc + a more specific specification for finishes, lighting , fittings, etc )
This should also help to inform the detailed drawings which you can use for building regulations and construction.
Finally make sure you get a proper contract. DO NOT pay up front for work - except possibly in the case of specialist fixtures/fittings which require to be made to order but you should get a letters and documents to back this up in case you have a claim.
good luck