First and foremost, the boiler manufacturer's warranty has nothing to do with the assessment process - the latter is to satisfy the requirements of the latest Building Regulations.
I recommend that you call the boiler manufacturer and ask them to confirm the terms and conditions, and duration, of your warranty, and what documentation the installer should have left with you to support any warranty claim (e.g. invoice showing date of installation). This should at least reassure you that you have a working and maintainable appliance.
Secondly, you need to make a decision regarding your installer. It's all too easy for us on the forum to damn him, but we haven't heard his side of the story. I'm not implying that you're fibbing, far from it, just that he deserves to be heard, even though on the face of it there's a rising tide of evidence to show he's not entirely trustworthy.
The question is: do you attempt to reconcile the relationship, firmly but politely explaining what you want to be rectified and why you want it, and give him a chance to put it right, or do you want to go down the adversarial path?
Before you decide, consider this: disagreements sometimes, but not by any means always, end up at court. If you're not prepared to go to court to uphold your rights, then you should be prepared to cut and run.
This is because the court will recognise the installer's right, as a trader, to be given the opportunity to put right whatever might be wrong with his work, at no cost to you. If you were to deprive him of that right for no good reason, then it would weaken your case.
Any legal professionals in this situation, would advise that you take professional legal advice. However, general advice is always as follows:
1. Keep a diary of events; include particular notes on the original brief that you gave the installer, any discussion of decisions that he offered you, and any requests you made for changes.
2a. Write to the installer, setting out your concerns. Keep it simple, and amicable - strive to keep all emotion out of the letter. Do your best to swallow your disappointment, because it's not a measurable outcome of the contract.
2b. In the letter, set out what you want to happen, and by when you want it to happen. Do not admonish him. Finish the letter with your expectation of the next step, e.g. that he contact you to arrange a date for remedial work.
2c. Offer to pay the installer in stages. A court will not see it as reasonable if you withhold ALL payment, since he has incurred expenses in buying materials. Offer to pay those expenses, plus, say, half of the labour, with the remainder payable when you are satisfied. Point out that you require the installation to meet the current Building Regulations - you don't need to know exactly what they are at this stage, but point out that you have a right to expect that the BRs are adhered to, and that any deviation potentially decreases the marketable value of the property.
3. Act swiftly and promptly at all times. Any delay may be viewed by the court as reticence and that you don't have the courage of your convictions.
The condensing boiler issue is a particular concern. You need to establish your own certainty about whether or not you have one (talk to the manufacturer), and, if you don't, ask the installer why you don't.
Keep under your belt, for now, the fact that, if the installer does not remedy the "faults", then, after he's been given a chance (or two), you have the right to employ another professional and to charge your man (or deduct from his bill) the cost of having someone else rectify the faults. I can give you chapter and verse on contract law if you would like, although I suggest it wouldn't be helpful at this stage, since you still have a chance to sort things out.
I write all this as someone who holds a rudimentary law qualification, and who has taken the route to court many times (mostly parties settle out of court, by the way).
Keep firm, but be polite, and you'll get there in the end. And there's always be help on this forum - we don't like tradesman who tar the reputation of the rest of us.
