Hello,
1)
"I was having major issues with the maxroam view app."
Maxroam app is not developed by Teltonika, thus I cannot comment on that in much detail.
"I was at a off grid place, when there was little to zero signal, my phone from time to time got signal, but the problem was the RUT240 did NOT connect, not even once."
It is difficult to estimate the exact reason without having the logs from the device, but, if the area you have tested your device in, really had almost no coverage, then the device may simply have not detected the signal. After all, it only has LTE Cat 4 modem, which lacks sensitivity and advanced signal processing features.
One thing that could be attempted is to try different LTE bands manually. For a guide, please refer to this video: https://www.youtube.com/watch?v=CAkjQ6a2qdc
"Another thing, I cannot connect to any existing."
Could you expand on what is it that you cannot connect to?
Also, is the place with almost zero cell coverage your intended spot for device use, or did you simply go there for testing purposes?
2)
"RUT240 uses a CAT4 modem, and most new smart phones use a CAT6 modem"
This assumption is slightly incorrect, as flagman smartphones can have modems with LTE categories 20 and above.
I get around 15-20mbit speed download, from the wifi from the router network.
If you are connected to the 4G network and 15 - 20Mb is all available bandwidth, devices connected via WiFi will not achieve greater speeds. If that is not the case, you can try logging to the router's WebUI, navigating to Network -> Firewall -> General settings and try enabling Software flow offloading option.
"My phone with the same 4g sim card, the same place gets 50-70mbits... CAT4 should be up to 150mbit, so the modem should not be a problem and I'm sure if I get the RUT360 with CAT6, the speeds should not be any different."
As mentioned, your phone likely has a more advanced modem and thus is capable of reaching higher speeds. The 150Mb is a theoretical limit achievable under ideal conditions, but in reality lower performance can be expected due to factors such as tower load, bandwidth, weather conditions, frequency, multipath fading, interference, reflections, etc. The major difference between Cat 4 and Cat 6 modems is that Cat 6 is capable to aggregate two LTE bands, meaning that it is most likely to achieve higher throughput simply because it can combine it from multiple channels.
"The RUT240 should be able to pump out 150mbit with the CAT4 modem."
Under certain conditions only, as actual performance is impacted by many independent variables.
Best regards,