Is it possible to use current custom DRC rules or need a new feature to define how trace can connect to a pad?
I refer to track can be connect to pad specificly 0, 45 or 90 degree only. Also avoid the trace turn right after it left the pad.
This could help to maintain equal amount of tenstion during reflow and allow better auto aglinment.
As for preventing components from beig lifted on one side (a.k.a. tombstoning), which is the issue you seem to be describing, you have to balance thermal resistance to ambient from both pads. Good rule of thumb is to match the track diameters on both sides of the component like shown below:
Large mismatch (avoid)
This is also the reason for using thermal reliefs whenever such components connect to a copper plane (since the plane has high thermal capacity, it will heat up slower and cause mismatch in thermals)
It might be possible to implement these checks using custom rules, but I’ve never actually used them myself. Either way here’s documentation for it: