Fundamentally, the only way for air to fill that line is if air gets drawn in somewhere, typically meaning fuel goes out too. Your pump would usually be a set of check valves, and shouldn’t allow flow backwards. Either the pump is failed open or partially open, or you have a leak.
2 other notes:
1- IF your pump is failing, it is possibly not moving enough fuel, thus simulating low fire all the time and contributing to your heat problem? It’s a possibility, although without seeing the system in person it would be hard to say for sure.
2- Technicality, but 5/16” = 8 mm, not 4, that is a huge difference in volume, so it could be useful to those helping you troubleshoot to know which you have. Guessing from looking at your pictures… 8mm line?