Since no one else will answer you I suppose I will.
I think you should post a replay if you're serious about improving your play so somebody can take a look at one of your games and give you pointers.
Now I ain't no HelpingHans but in regards to your comments:
1) I find this to be untrue. In my experience I find the mortar pit to be the most cost effective mortar in the game because it doesn't bleed any manpower and can just be repaired. It does not cost more than double the Ostheer mortar as the mortar pit is 400MP and 2xOstheer mortar is 480MP.
I've never used the base guns yet but I have seen them used to good effect vs OKW trucks + a primary assault. If you have need of flamethrowers and rocket artillery you really should be picking the commander that has the flamethrowers and the land mattress. I know a lot of players complain that you have to pick a doctrine to be able to counter game mechanics but that's just the way it is man. Doctrines exist to fill gaps in rosters and to be used as a response to what your opponent has done, this is true for all factions and in the case of your opponent having an unkillable pak wall and a bunch of garrisons, the land matress is the counter.
The mortar pit in general is actually great at countering other mortars, but I understand that defending emplacements can be difficult when your opponent really goes all in against them. You really need to have an MG and an AT gun around an emplacement to make a strong defense. As a tip, UKF AT guns can shoot through their own emplacements but not get hit in return as the fire will hit the emplacement instead, so position your AT gun behind your emplacement.
2) The UKF sniper is difficult to use, I can agree with you there, but I also kind of love it. A sniper and an IS can completely wreck a Kubel which is actually a huge problem for OKW because the Kubel is their sniper detection unit but dies so easily to one. Use a lot of mines to cover flanks so you don't get 222'd or luchs rushed, you should have a lot of munitions free for mines most of the time. The sniper's stun shot is straight up OP when combined with other units like the firefly. I've insta-killed tigers from chain stuns(sniper + firefly) and an AT gun.
Regarding the AEC, I'm actually consistently surprised with how well this thing does against infantry considering how excellent it is against armour. If you're having trouble vs light armour even though you have an AEC I would suggest getting a 6 pounder, the two of them together basically instant kill light vehicles like the luchs. You could even try to bait your enemy into one by over extending with AEC and having the AT gun into position when their light vehicle comes in for the kill.
The bofors can fire the suppressive barrage if it's garrisoned and target the mortars firing at it. But yes, they will die fast if they are left unsupported, Which is why if you're going the bofors route (wouldn't suggest it in 1v1 against competent players) you should also have the mortar pit. Your opponent will only be targeting one emplacement at a time most likely so the pit can be raining shells down while the bofors takes damage making it difficult for the enemy to stand still to shoot. Combine this with the stand fast doctrinal ability and it becomes so difficult for the enemy to destroy an emplacement, not to mention brace.
In relation to Soviets, if you enjoy them and their playstyle more then just play them instead of getting frustrated.
Brits are their weakest in the early and early mid game but it appears you play mostly 2v2 assuming this is your playercard:
https://www.coh2.org/ladders/playercard/steamid/76561197978313162 so why not combine them with a teammate playing US to fill the gaps of their weaker start?
3) This is pretty much true (with a few exceptions) for all factions in all cases, you just learn them with experience. Yes Brits are easier to predict because they have fewer optimal build orders, however if one faction has 3 and one has 6, but you already know them all by heart, then what's the difference?
There are always exceptions to this.
4) Without seeing a replay it's difficult to suggest advice vs specific issues.
You mention that it feels like the faction relies on the enemy screwing up which I find funny because I feel like the only way to win against Brits is for the Brits to throw their toys away in stupid plays.
Some random things:
Royal Engineers are OP as fuck and you should have a bunch of them. They are so cost effective, especially with their vet bonus, that there really is no reason to not use them. I normally only ever have two squads of Tommies and often 3 Sapper squads.
Good sandbag play is a requirement of Brits, if you don't use sandbags it's really no wonder you feel like Tommies suck. Build sandbags against strategic point flags so your side gets cover but not the enemy's. This is important to do if you push your enemy off his cutoff or fuel so when he comes back he has to fight into green cover bonus tommies. I would avoid building sandbags on your own cutoff as occasionally the enemy can benefit from them and then you have to fight into green cover (often on negative cover roads) if they ever secure your cutoff.
Build trenches on VP's (not the center one on most maps) or on your opponents fuel or even your own fuel if you feel like it will come in handy later. Trenches are pretty cheap, just be careful about spamming them in the early game or else it will mess up your unit timings. I would avoid putting MGs in trenches as they have a blind spot and will probably just get flame naded, however putting an IS in them works very well.
Don't throw your shit away in stupid plays. I see Brits players of all skill levels do this constantly. You get your nice, shiny, fast and effective Cromwell and you see that stupid P4 out of position and it's just so JUICY you need to go in there to blow it up - whoops - there's a Pak - whoops - there's a faust. Just play conservatively, only go for something if it's a sure thing.
All I can really think of, I only play 1v1's so this is from that perspective. Hopefully that helps but keep in mind I have no talent.