If people are still under notice period normally they have full access to the internal internet as this is required for day to day operations, emails, rosters etc etc. An exception may be if a guy decides to leave, gives 2 months notice, then goes sick, or leaves the country permanently for the entire notice period. In this case there is no reason for him to have access to the systems.
Selective removal from the ID travel system takes positive intervention by HR and this would only be done if there was a reason ( abuse, or as above)
Regarding " exit strategy" simple, when you join you sign a contract, that sets out the terms for leaving and any penalty involved ( balance of training costs, salary penalty, notice period etc)
When I say the " Turkish culture" I am referring not to individual attitudes but the red tape and bureaucratic process that newcomers often find frustrating. For instance you cannot start " training" until you have a work permission, this is linked to your resident permission and can involve trips back and forth to your own embassy etc, in your home country. This is often seen as favouritism towards the Turkish pilots whom are excluded from this process and can thus start training much sooner.
This is huge airline, you will not be a cosy relative of the management, simply a number and a resource, if you take that attitude and accept it, it can work. Expect no favours and if you get any its a pleasant surprise.
In terms of "support" for families, finding schools, housing, etc, I have found the Turkish FOs and colleagues always willing to help, make calls, arrange visits etc, but the HR department is not focused on this area as it is not their responsibility.
If you are prepared to help yourself, things work, on the other hand if you expect to me spoon fed solutions, it does not work.
Personally, I can adjust, my expectations after 6 years are less than when I joined, on the other hand I keep things simple.
A typical issue would be " moving house", this would involve lots of paperwork, visit to Police, Bank, Notary, Cable firm, Water, Electric and trying to get the deposit back from a Landlord is like getting blood from a stone, so its annoying.
In this respect, it may be better to do lots of research before renting to avoid the issue all together, if you rent an old place, chances are it is due to be knocked down.
As observed by others " training standards" can be exacting, and many ex military guys lack the advanced CRM enjoyed in the west, but this is partly a language confidence issue as well.
As for leaving your other job.. thats a decision only you can make..