Yes you'll need a coupler so that you can move the tee further along. If it's an uncommon sized waste connection and you're determined to keep that it, keep the tee and reducer that are there, just move it along with a coupler and a new piece of 110mm between the coupler and the tee.
No you don't absolutely have to move the tee(although you will need to rotate it), but you are risking future problems by having the tee and a flexi which will create the equivalent of 3 90deg bends in a very short run of soil.
You may even get poor flushing from day one if you do it that way. A rule of thumb with wastes and soil is to have as few bends as possible.
If it was me, and that waste is an unusual size, I'd re-do the waste from the bath in standard 40mm solvent weld bossed into the soil in a similar way to how the 55mm is currently connected.
Then I'd connect the basin waste into the soil behind the wc on its own boss to help prevent the bath pulling the trap of the basin or vice versa (I'd have anti syphon traps on basin and bath if possible for belt and braces).
The 110mm tee would be directly behind the loo with a bent or straight pan connector - whichever one is needed.
I'd say a maximum of an hours work if you have everything you need to hand, and there's very little risk of problems if you do it right first time.
I have a very similar setup in my house where I have vanity wc and basin next to each other with the basin waste bossed into the 110mm soil, it works well, although my bath has its own waste run.
As for the 1m flexi to feed the wc, I agree that flexis make connecting to concealed cisterns a lot easier, but why not hard pipe it to 300mm from the cistern connection, then use a 300mm flexi tap con. Will mean a lot less weight pulling down on the fill valve which is only supported by a thin plastic cistern wall.