the green colour of the cylinder will be the factory-applied coating of rigid plastic insulating foam. Poke it with a thumbnail and it will leave a mark. Green means it might be about ten years old, and while not as efficient as the latest blue ones, or a white one, is OK. It will have large copper pipes going into near the bottom and near the middle, these will be very hot while the boiler is heating the cylinder, so should be insulated with foam lagging such as Climaflex or an own-brand alternative, as thick as will fit, on the pipes around the cylinder and around the boiler. This is a cheap and easy DIY job if you have a breadknife.
The Mexico 2 I can't find, there area lot of Ideal Mexico models, ranging in efficiency from about 70% to about 80%, it is a non-condensing boiler and I will guess has a cast iron heat exchanger and will be simple and not much to go wrong. A modern condensing boiler would be about 90% efficient so could save you between a seventh and an eighth of your gas usage. This alone would not cover the cost of change, but will be a benefit when your old boiler dies.
It is likely that with this old boiler, even if it is running well, by this time there will be a lot of sludge and scale in the system. For example, you might find cold patches at the bottom or the middle of some radiators, and the boiler may bang when hot, or make a noise like a singing kettle coming to the boil. It can be cleaned out in various ways, of varying cost. Cleaning it out will improve the efficiency and economy, as well as giving greater heat from the sludgy radiators, but I can't quantify that.
If your TRVs are equally old, they may be sticking or failed, so that they no longer maintain rooms at the desired temperature, so reducing comfort or economy. It is fairly easy and cheap to change them if you are fond of DIY plumbing, but will be fairly costly if you have to pay someone. It is best done in the summer when heating is no longer required.
Your house will be warmer and feel more comfortable if you carpet those wooden ground floors. If you have access underneath them you can insulate between the joists. This is laborous and dirty unless the floors are being lifted for some other reason, for example they are chipboard and are being put on the bonfire.
Some people will tell you that you need to change to a Combi boiler, this is not correct. Modern condensing boilers are available as Combi, heat-only, or conventional, and you are free to use a HW cylinder of various kinds.
If you block up the ventilation holes in the room with the fireplace, I am sure you will forget to unblock them if and when you or a future person lights the fire again. A local chimney sweep can advise best on how to handle the chimney to prevent draughts, and what ventilation is required. He will also know if you can DIY, and he will know who are the local tradesmen who will make a good job of it.