Firstly I'm not a plumber but I am a professional working in the building industry, working for a large contractor. As a "hobby" I do my own plumbing and a few nixers also. I'm very familair with the Building Regulations and the Bord Gais installers manual. Now to address some of your concerns:
Every plumber has his own way of doing things but-
1. You say the original installer seems to have made no provision for the new gas feed. I presume the original gas meter and shut off position are unchanged? I also assume he wasn't intending on routing the new gas feed externally (unusual in a domestic situation). You are entitled to ask why this has been overlooked, surfaced mounted pipework is not acceptable when the opportunity to conceal it was readily available earlier in the job. Very hard to comment authoritively without seeing the job.
2.As for feeding all appliances directly off the cold water mains, this is definitely a no-no. If the main supply were interupted (during a dry spell or maintenance for example) there is a possibility that dirty water could be drawn back into the mains by back siphonage, this is particularly the case with bidets, wc cisterns, wash basins and the like. However, occasionally I have come across a downstairs toilet which had it's cistern fed directly off the mains, as I say not good practice but if the cistern were fitted with a double check, non return valve the risk of contamination would probably be nil. Also the high water pressure would probably shorten the life of the ball valve. In the ideal world only the main drinking water tap (kitchen sink and maybe cold tap on utility sink also) plus the cold feed to the storage tank in the attic, dishwasher and washing machine should be fed off the mains supply. Toilets and wash handbasins should definitely not, their supply should be from the lower pressure cold water storage tank only.
3. As for wastes this is a personal preference issue. Presumably the hoppers you refer to are to be located externally with 40mm white wastes punching thro' walls and discharging into same? This is the traditional way of plumbing waste pipework, it doesn't look as neat (maybe) as the strap and boss method but it does work and there is probably less likelihood of blockages, plus access for cleaning, if needs be, is easy. The strap and boss method is a more modern approach, brought about by advances in plastic plumbing in the last decade or so, but for it to be effective proper traps are necessary, especially on showers.
There probably is no absolute right and wrong here, without seeing the job it's very hard to comment on competency here, but good neat plumbing, with pipe runs well laid out and crossing pipes and joints kept to a minimum is pretty easy to spot. Bad plumbing could mean- pipe runs badly laid out, taking up a lot of space, too much jointing compound/ tape visible, too much plastic (subjective), lack of isolation valves, lack of clipping/ unsupported runs etc. Basically bad plumbing, to my eye anyway, is a constant visual irritant in addition to being "bad".
Meet with your original plumber, ask some pertinent questions, you'll know by his demeanour whether he is competent and confident to undertake the work. Whatever you do give him the right of reply.