1. I wouldn't personally describe Buttler's keeping as below average - he's not incredible but he's generally fine. This match was obiviously bad but I've got no particular worries that it's a sign of what to expect from him for the rest of the series. Until 3 tests (sort of 2, but the 2nd WI test didn't really tell us anything either way) ago I was fed up enough with his recent poor batting to want him dropped from Foakes, but I'm happy for him to stay after his improved batting since then. I do think Foakes is a better keeper and probably a better bat overall, but he hasn't been in good form recently so between that and current lack of match practice I don't think the swap is worth it now that Buttler's doing better. If Stokes is fit to bowl again, presumably Buttler will be at 7, and his batting overall is fine for a #7.
There was a gap of 15 innings between Buttler and a 50 or more score and 8 of those innings was less than 30. That is abysmal batting. In terms of keeping, he is below average, an average keeper would be someone like Paine, who is very much on the wrong side of 30 but still more athletic and safe than Buttler. Compare him to more athletic keepers such as Rizwan and you see that England have a deep problem here, especially one made worse if they really want a full time spinner. Keeping to spinners is much harder.
2. I'm not sure of Jimmy at the moment. I'm not going to say he's finished (which I've done before and ended up looking silly). I think his current meh-ness is due to his age and circumstances combining to slow his return from injury. In general, if he does get back to near his best, I'm absolutely fine with him only playing in 1 or 2 tests a series if that's how things have to be done from a fitness management POV. I appreciate the need to give the next generation a chance but you pick a team to win each and every test imo and that means selecting Jimmy if he's anywhere vaguely near his best.
I think Jimmy probably has enough in him to last till the next home summer, minimum BUT keeping don't like the idea of keeping him around in expense of a young, fit, swing bowler, whoever that may be. Especially as Jimmy still has the shadow of away tests hanging over him. He still averages a whopping 33 away from home and hasn't been fit enough or maybe good enough, to play more than 7 tests away (terrific in SA but it was a rarity compared to the rest of his work). Why not bleed in someone new? Again, I repeat, I think he is good enough to carry on but that may not mean he should at the expense of someone potentially younger and better.
Curran will always be in contention for home tests (even though I remain a bit unconvinced by him) and I imagine Jimmy will retiring anyway before too long (I know he's said he wants to do the next away Ashes but that seems pretty unlikely imo) and Curran will probably get a pretty extended run at that point.
Archer at this point just needs more test experience imo. He's shown already that he can absolutely deliver at this level and I'd be more inclined to stick with him whilst he learns than I would with Curran tbh.
I'd stick with Archer too but his attitude needs a change. He seems kind of moody now that he has solidified his test reputation against Smith.
Wood in England should just be a no-go at this point. I think his stats are a bit blown out by him being selected when he shouldn't have been, but he's never had a particularly huge impact on any tests he's played at home, happy to keep him on the radar for away tests though.
Strange....he had 20 wickets in his first home run, injuries and being dropped have hurt him and his home come back may not be great but he has shown he can perform here and should be giving backing if Archer isn't good enough or motivated enough.
3. I think what Howe said in the tour thread is largely correct, in that there does seem to be a bit of a hindsighty pile-on on his captaincy sometimes. That said, I don't think he's especially good tactically regardless, so if we could shift the captaincy to someone else (would opt for Burns over Stokes personally) it would be worth it if his batting improved as a a result
Many have said Root isnt a good enough captain for a while. I remember discussing with friends post Cook, would Root be an inventive captain or a defensive, often reactive captain like Cook. Sadly he has been too much like Cook, which is weird as Root's peak batting was so inventive and attacking and going for the kill. I'd rather Root the batsman than the captain.