True, there are so many scenarios that the rulebook doesn't specifically cover
But most of the points you ask are specified in the rulebooked. Taking this rulebook (Anniversary: compliance with srping 1942 edition) for instance:
A transport can move between one or two spaces that do not contain an enemy surface ship during combat or non combat phases. It can load and offload units into free cargo slots before, before or after any of the previous. However load and offload procedures cannot iterate (you can't offload units first and then load). Offloading units ends the transport's actions: If you begin by offloading units of a transport (loaded in previous rounds) then the transport will not move nor load after that.
Other rules apply for a transport engaged in combat.
A unit(s) is loaded onto a transport that has not moved yet, then the player moves the transport
As long as the transport did not participate in any combat this round, it can be moved, loaded if it has any valid free space and offloaded. It cannot iterate load and offload.
A transport moves one space, then picks up a unit and moves another
It is valid as long as the first move does not put the transport in a seazone containing enemy surface units (thus putting it in combat)
A transport moves one space and then bridges a unit(s).
A transport moves two spaces and then bridges a unit(s).
If bridging means moving land units between adjacent territories in a seazone, it is valid. The transport has: moved (one or two spaces), loaded and offloaded (one or two units).
If between move and load/offload the transport moves to an area with enemy surface units, then the sea combat mus be resolved first (amphibious attack)
Remember that no unit can move to any other territory containing enemy troops during non-combat move phase; except for submarines.
A transport moves into a sea space where an enemy has a submerged
It can be done either in combat move and non-combat move. If done during combat, and you move along a destroyer you CAN choose to engage or not engage the enemy submarines. If you choose to, the transports take part in the combat.
A transport bridges unit(s), after battle proceeds bridges unit(s)
again to a different country (this is complying with the rule that
says you can only attack a country once a turn).
No, for two reasons.
Transports that engaged in combat cannot do anything else after (move, load offload)
After offload, the transport actions end.
An airplane (usually a bomber) comes from the land and bombs an
unguarded transport and kills it
If the question is: "Can the transport be destroyed?" the answer is: yes. It is automatically destroyed during combat resolve phase.
I would suggest you install tripleA. It is an open source game that can implement A&A ruleset and its different maps; the rules there comply pretty well with the rulebook.
This were many questions packed in one.. :/ I'll later add the pages refferences to each sub-answer; or I would welcome anyone editing to add that info.