Macharias the Mendicant said:
Generally, a SM can only benefit from ONE squad mode ability at the time (even if more than one are active and sustained by the Kill Team). I would interpret that he can chose to use a Solo Mode ability INSTEAD of a benefiting from a Squad Mode ability. So, in your example, I would make the character choose between the two. Essentially, he'd be using a Solo ability AS a Squad ability (ie: spending cohesion), hence why I'd make him choose.
I know that RoB allows a PC to spend cohesion on individual Solo abilities, but Cohesion is supposed to be about teamwork. As bogi_khaosa said, spending on SOlo abilties too often won't make the kill team happy. It should really be reserved for those desperate situations where no other options exist.
RAW, to me, indicate that one could benefit from both solo mode and squad mode abilities- the rules only say that you can activate a solo mode ability at the cost of cohesion, but I can't find any reference that says you can benefit from one or the other, just that you can't benefit from more than one _squad_ mode ability at the same time.
RAI, on the other hand, appears to me to be a clear case of only allowing the Marine to benefit from one 'special ability' at a time- thematically as well as balance-wise.
In my games, I only allow players to benefit from one or the other, never both. If you want to use Feat of Strength while the rest of your squad uses Fire for Effect, go for it- it'll cost you cohesion and you can do one or the other, not both. That would also mean the subsequent turns, while Feat of Strength is still active, you can't benefit from any other Squad Mode abilities that have been called or are being sustained.
As for activation cost and keeping things active- it depends on the ability. In the case of Siege Master, based on the entry description, I'd let the player spend the cohesion to activate it, and they could maintain it so long as they remain stationary. They could even alternate turns as to which ability they benefitted from (squad mode versus solo mode) if applicable, but in a given turn they could only reap the benefits of one ability. As soon as they move, it turns off and if they wished to activate it again, while in squad mode, they would need to spend the cohesion again.