This issue is fixed in the build 14936. Here is what it says,
We fixed the issue causing the pin pad to not be visible to unlock the
phone even after rebooting the phone.
We fixed the issue where some phones lose the ability to use their SIM cards.
Windows 10 build 14936 rolling out for fast ring insiders.
There is no option to select what to use on what connection. when you enable your cellular data connection it is used for all apps you have selected to be online. being it mail sync, facebook chat or background agents of apps.
for example your mail will keep syncing if you're not on wifi. same for facebook connection you'll stay online when you are on 3g ...
Several reasons what is wrong:
The device is locked to be used only for specific SIM
The device is set up to manually search and register to another network (other than T-Mobile)
Settings - Network + SIM - Setting of SIM - Search automatically for network
The SIM is somewhat wrong (blocked, or inserted wrong way)
Try switching between using the older network standard and the newer on the phone, and then see if you can visit websites using the newer after that.
If that works, then maybe Microsoft (or AT&T since it can be a problem with them) will listen to you if you report that.
Try setting up an access point manually from settings section. Before that turn off cellular data.
You will be required to go to, settings >> access point. Tap "add" application bar button. Give your access point name (you will get it from your operator, in my case its "blweb" as my operator is Banglalink3G). fields like username, password, proxy address, ...
Follow these steps:
Settings > Network & Wireless > Cellular & SIM > Click on 'SIM settings under category SIM > Click on 'Search for networks' under category Cellular network > Wait for the searching and then select the operator you want.
You say that you are using "the latest windows preview" and your title says "10.0.10586.36".
As of 5th February 2016, the latest is 10586.71 (Slow Ring), as announced in the Windows Experience Blog.
First, if you have still sometimes access to the network, check for updates.
If you are in Slow Ring, you could also try the Fast Ring.
It is also possible ...
Fist you must install an another browser(like UC browser, Opera Mini-beta, etc..)
Then go to windows mobile storeby using your new browser.(Don't use Internet Explorer. It will automatically connect you to your store app)
search your app
In search result choose your app that you want to download
Then they provides you app details like in store (...