Can I use this to run my own mobile network? Is there something like a blank SIM card which I could use for it? I don't need global coverage but is it possible to create my own BTS on a PC (with some antenna connected to it) and then have my own SIM card which I can insert into regular phone/device and have it connected to my BTS and connect to the Internet?
Yes and yes, although in most parts of the world it won't be legal when done via antennas. You can buy blank SIM cards from vendors like Sysmocom, which are preprogrammed but "writable" SIM cards. The important part is knowing the private key that is used to authenticate end user devices.
Then you'll just need a decent SDR and it actually works fairly well for small test setups.
Nitpick: in most places you need a license to do this with antennas (in some places temporary licenses aren't that hard to get for temporary/noncommercial use)
Do you have an idea what would be my external IP address? On my phone connected to a mobile network, I get assigned mobile IP address which is my external IP address. It's not attached to the SIM card because it changes when I reconnected. Is it handles by the BTS software? Do I get assigned an IP address and BTS communicates on my behalf using that address which comes from the mobile network operators pool?
The LTE core assigns an IP address to your SIM card/UE. In the case of srsRAN, there's a simple CSV file mapping the IMSI to an IP address, but there are no limits on how complicated it can get.
Yes, is simple enough to get started if you have access to the required hardware. You might able to operate in the n41 band (2.4GHz, like wifi) even without a license.
Phones are nitpicky about network configuration (chippers, emergency calling and so on). I would recommend starting with a USB modem. Also setting your network PLMN to the 00101 (the testing one), as it usually gets preferencial treatment in UEs.
N41 isn't 2.4ghz. It's licensed 2.5ghz. You're thinking N46 which is unlicensed 5ghz.
LTE didn't allow for it to be used as primary carrier, but NR-SA I think does.
This site[1] details setting up an LTE network, including programming a blank SIM.[2]
[1] https://www.quantulum.co.uk/blog/private-lte-with-limesdr-an...
[2] https://www.quantulum.co.uk/blog/private-lte-with-limesdr-an...
The hard part will be legal. You will need permission to have a radio and that often means certification of the system along with right to use the frequencies phones use.