Boiler efficiency question?

[stressedouttumbleweed]

We have a new system boiler. We have a smart thermostat system, with smart trvs on 5 radiators and 9 rads with regular trvs.
If only 1 trv is asking for heat then all the rads with regular trvs are on.
Question is-does the boiler have to work harder to heat 10 rads vs 14? Ie does it actually save any gas at all to have individual rooms set? The rads that don't have smart trvs are pretty small/towel radiators whereas the other ones downstairs are big (9000BTU)
Does that make sense? Also is there much difference in having water set to heat twice daily for a short time vs once for longer? We have showers in AM & child has bath in PM so need water at both times, plus washing. It's a 220L unvented cylinder.

Question is-does the boiler have to work harder to heat 10 rads vs 14? Ie does it actually save any gas at all to have individual rooms set?

The boiler has to work harder to heat 14 rads than ten. The extra heat being dumped into those four rooms has to come from somewhere. If 14 rads are on then the water returning to the boiler will be a bit cooler than if only ten were on, because more heat will have been lost as the water goes through those extra four rads, so the boiler has to burn more gas to get the water back up to temperature.

Also is there much difference in having water set to heat twice daily for a short time vs once for longer? We have showers in AM & child has bath in PM so need water at both times, plus washing. It's a 220L unvented cylinder.

Probably makes very little difference. If the cylinder is well-insulated the water will stay hot for a long time, and little heat is lost, so whether you heat it just before you use it or several hours, doesn't make enough difference to worry about. And anyway, any heat lost from the cylinder contributes to heating the house so the rads have very sightly less work to do and it balances out.