Granite [SVK]

Try disabling speed limiter in singleplayer, either through game settings, console commands, or shut down the game and manually change it in config.cfg.
You can also check config.txt located in "User\Documents\ETS2MP" or "User\Documents\ATSMP" and search for this line and make sure it looks like this:
"use_speed_limiter" : false,
Start the game via TMP client, log in and do not touch speed limiter in game settings, for me it always shows up as enabled no matter what, even though it's disabled.
Check TAB setting if speed limiter is disabled, it shoudl be, now you should be able to reach speed limit set by server, or go as fast as possible on arcade servers.
 
Keep in mind, TruckersMP does not overwrite your local config files, but some game settings are handled differently, or duplicated by TMP, like the speed limiter.

Unrealistic? I don't think so, wet road surface has huge impact on braking distance, even moreso when your weight is 40t.
However, tyres make a huge difference, choose those with best wet grip (braking) rating if you are playing ETS2.

If you don't own eiter Michelin or Goodyear DLC  which both offer excellent choices, you can pick "Elemental" tyres which are the best in the base game.
In ATS all the tyres seem equal, they don't have this label system in USA, but they all seem to perform better than basic "Trailmaster" tyres in ETS2.
 
Speeding and late braking should be avoided. With gradual and early braking you can even use retarder or egine brake without problems.
 
As far as I know you can't alter rain physics without modding the game, but you can always put rain probability slider all the way left in game options - no more rain.

Looks like you can't find it, because that TMPID no longer exist, meaning that account has been deleted, probably at the request of the owner.
 

That area is edited by Truckers MP, including that road sign, some stone walls, fences, guard rails and those billboards on the overpass. Nothing of that will appear in singleplayer, because it's part of the mod.
They have probably intended to add traffic lights as well, but changed their mind since they would be ignored by just about everyone, and forgot to remove the sign.
 
I would make it a toll road and add toll gates at both ends and at the two exits in between.

OK, the easiest way  Ican think of:
 
Open config.cfg located directly in Documents/Euro Truck Simulator 2 folder
Search line:
uset g_developer "1" - if the value is "0", change it to "1", save and exit, this will enable console commands in-game.
 
Now start the game (singleplayer or multiplayer, doesn't matter, only multiplayer disables certain ommands that could be abused for cheating/trolling) and load your profile, you can press drive button to spawn in your truck.
Press tilde key (~), the key directly bellow escape key, a console appears in top left corner.
Type :
g_simple_parking_doubles 0
press enter, then press tilde key again to close the console.
 
Now skilled parking should be enabled for doubles, if yes, save the game and the setting will be kept unless you load older save.
 
ADD:
It's actually 
g_simple_parking_doubles 0
sorry.
Some prefabs may not have hardest parking option available, not completely sure about this.

1. No, there's no restriction zone for double trailers.
 
2. Not without save editing, by default, you can only make deliveries withing countries where doubles are allowed - Scandinavia, Germany, Netherlands and Finland (HCT only in Finland)
You can try this save editing guide:
 
 
3. Yes, rules are same for any trailer, there are no restrictions.
However if your trailer is save edited to be longer than default trailers, or combines trailers of different types, or is not standard in any way, it must comply with paragraphs  "§3 - Save Editing" ,and 
"§5.1 - Server Auto Kicks" -  max 3 parts trailer in ETS2  (trailer part includes dolly, so HCT are trailers with 3 parts, standard doubles and b-doubles are trailers with 2 parts)