Hi there. My son passed the Hall 5+ assessment this year so he'll be going there next year. From what I gleaned things checked are: ability to concentate and follow instructions (teachability is the no.1 trait schools are after; so ability to conentrate and follow instructions cannot be overemphasised); responding to questions on a story read; phonics, letter recognition (e.g. they show them a word and they tell the teacher the letters), patterns/sequences, draw a picture; know their address, be able to talk about their mum, dad, family, rhyming; odd one out; simple IQ stuff. My son is confident and could read at the time of the assessmetn but I am not sure they asked him to read. I am not quite sure if they asked him to write his name either. They probbaly did, so you may want to practice that. They do a number of activites with a number of teachers (4 I think it was) on a 1:1 basis. The assessment lasts about 40-45 mins, so I guess they spent about 10 or so mins with each teacher on each set of activities. They have a drink and biscuit half way through and this is what my son remembered in the main. Plus the knight toys.
The Arnold House one is a 20 mins affair and usually siblings, alumni kids, kids with connections to the school get priority. Puzzles, Q&A on a story is what he recalled.
Devonshire again is a 20-30 mins affair. Not that rigorous (although my son did not try it). I would not avoid it. Check out the destination schools and you can decide on the basis of which senior school you are after. That said, quite a few of the Devonshire boys leave at 7+ for UCS, Highgate, Westminster etc.
Arnold House and Devonshrie House have very similar exit results for boys, (and similar intake).
Mulberry House is one to go to if you are after a 7+ transition. They prep the boys for 7+ entry at UCS and Highgate in the main (but not only). I would be surprised if they have 4+ opening but you never know. If your son is being assessed, they clearly do.
Similar to Mulberry House is Hamsptead Hill in NW3. More nurturing than Mulberry House. Excellent 7+ (and 4+/5+) results. Hope this helps.