Based on the TMG log you attached I do not see where it is having an issue. Initiated and Closed are normal. I am not seeing a "Failing" or a "Denied". You may want to address that "Resource Allocation Failure" which is usually
caused when IIS is running on TMG. If IIS is running on there disable the IIS Service and restart the machine. It should resolve that error. You may also want to reset all those Alerts and see which ones come back.
The only way to really know what is going on is to get a network trace from as many points on the network as possible. So 1.)client 2.) Internal TMG NIC 3.) External TMG NIC would be a good start. Match the network tracing up with TMG logging and see if
there is anything odd there. I do not know anything about Telegram or what ports it should be using but based on your Access Rule everything should be going out through TMG as long as they are NAT clients.
It also looks like some devices on your network are triggering Flood Mitigation thresholds. Review those IP addresses and if they are expected to be generating a lot of traffic you may want to add them into Flood Mitigation settings as Exceptions.