Is cold water flowing in to a tee like this ok?
Similar could be said if any cold supply is used whilst on is in the shower?Yes.
Bear in mind that if the toilet is flushed whilst the shower is in use then there will be an effect on the cold flow rate.
(sometimes, for reasons best known to themselves, it's easier for people to make clever comments rather than provide practical help!)
So you recommend teeing off the hot and cold main supply's separately again to pick up a shower?It's less than ideal but in real terms it will make no difference to your install.
Preferably from supply through the long 'T' section with a riser on the centre to your first appliance to your second appliance with a pulled bend to the connection point. If possible/practical it's better if showers have a supply independent of other appliances.
(sometimes, for reasons best known to themselves, it's easier for people to make clever comments rather than provide practical help!)
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