Since Issue Number 1 happends because of upgrading your Iphone, the logical step is to downgrade or return back to the last system you use which works well. Unlick, microsoft or windows it has an option to "system restore" which you can choose a restore point on which your system last time works fine.
In Iphone softwares it is not as easy as just changing or resetting to return to the default system. In you Iphone Settings and Generals tab you can find to restore or return to the default settings menu. This works on your iphone but its function is to restor profile or standard settings functions of your iphone only, and not restoring its previous OS or IOS and it will not downgrade your baseband. Baseband is a modem firmware use by iphone to connect to your telecom operators, however other new OS cannot work on old firmwares since its basband is high so you need to downgrade you OS.
There are 2 ways to downgrade your Iphone:
1) You can use your standard itunes to downgrade, by just connecting your cable from your iphone and wait to synchronize. On the menu there is an option to upgrade iphone and synchronize (of course you will not do it), and the other option is to restore (return to default settings).
Before you choose to restore make sure you downloaded the previous ".ipsw" version of your phone, or which version you remember it works well. You can get all .ipsw version by searching in Google or go to iphone website and search ipsw. The examples of ipsw versions are "60.ipsw, 4.1.ipsw, 6.1.ipsw, 6.1.3.ipsw...etc.)
Download the ipsw of your choice and save it to your most secured folder of your pc. You might notice that when you download the ipsw files, some website offer this or converts into ".zip" files. Don't worry, website made this to lessen the size of the ipsw.., Just download even if it is zip files.
After downloading ipsw zip file, you can just remain its extension name from .zip to .ipsw so to be recognizable in itunes.
When download completes, you can now open your itunes and wait to finish its synchronization or settings ups, in order to restore to old ipsw version, just pres "shift + click" the settings restore to default or return to default settings. This will let the browser open and you can choose your downoaded .ipsw. Before you continue make sure that your antivirus software should be unabled and should be marked as not live, this is to avoid errors while you are restoring.
After choosing your previous .ipsw, now it would install be itself and may ask you to back up and restore, it might let your phone restart for 2 times.
The issue of "No Service, Searching..." should be solve if you have upgraded the open line Iphone.