We only carry out cleaning hence have not registered for CIS, however some clients have asked for CIS we simply explain its not required for 'cleaning only', last time we checked with revenue .... so far no probs !
prefer to have money in my back pocket 
Your accountant is going to have fun
The only issue with not being CIS registered for some companies is that their billing is set up to automatically deduct CIS. It is therefore so much simpler to just insist on CIS accross the board.
If you meet certain criteria you can apply for CIS exemption but best to check with existing Clients / target Clients that this wouldn't exclude you from working with them. Even if you do meet the criteria it is far from assured that you'll be successful.
Onto the original poster: -
1) VAT does not apply to new build houses, so double check it applies to this property.
2) Depends on your knowledge, experience and capability. Only you can know this.
3) Sub-Contracting - It is unlikely that you're the only company invirted to put a price in. Margins being what they are I doubt you'd compete on price with a mark-up added. Other issues are insurances, payment terms, quality, reliability, liability. This list is endless. Best chance for you here would be to speak with those here showing an interest. Check their previous work (references). Agree a fee for yourself should they suceed in winning the job via their own tender. This way you have no obligations, nor liabilities to the customer as you are out of the loop.
Just be sure to get the agreement nice and tight.