Legions operating together in Britain?

[Nathan Ross]

the Fourteenth... had a number of Batavians attached to them during the Boudican uprising

The eight cohorts of Batavians were actually 'attached to the Fourteenth' in the context of the civil war in AD69 (Tacitus Histories I.59) - it's possible they had been attached before this as well, and since Batavians seem to have been involved in Plautius' invasion and Paulinus' attack on Anglesea, these same cohorts may have been with the legion the whole time. But it's interesting that that these particular Batavians seem to have got on very badly with the Fourteenth, even fighting with them when they shared a camp. I suppose it's not unknown for units that serve together for a long period to end up hating each other's guts, but it's also possible that these were different Batavians, and/or the Fourteenth had other auxiliaries during its time in Britain.

Regarding artillery, would there have been specialist units or would each Legion have contained its own?

Vegetius (II.25) says that each century had its own carroballista, and each cohort its own larger stone-thrower (which he calls an onager). This is a late source, but Josephus has Vespasian's three legions in Judea mustering 160 artillery pieces between them, so the numbers could be accurate for the first century as well.

This might not mean that each legion carted all this artillery about with them everywhere they went though - perhaps the machines from each legion were grouped together under a separate command?