Starting a Sentence with a Conjunction [duplicate]
Solution 1:
Coördinating conjunctions, such as and, or and but, can be used to begin a new sentence. This was already widely accepted in Fowler's time, and probably always. There is nothing wrong with the conjunctions in your examples. In general, though, you should apply this feature of our language judiciously: do not do it in every other sentence.
However, you should not use a comma after such conjunctions the way you did. Some authors use commas there, but be prepared for some criticism; it looks very casual. The exception is when what follows is parenthetical, such as in this sentence:
But, even though I like her, I must leave now.
The clause even though I like her is marked off by commas, the first of which happens to come after but.
You can always begin a sentence with a subordinating conjunction, such as because, although, etc., provided that the subordinate clause is attached to a main clause. If you don't attach it to a main clause, it becomes less formal, which may or may not be appropriate, depending on the genre.
Solution 2:
I, while accepting the idea of starting conjunctions, can't quite applaud your own sentences here.
I'd say the suggested conjunctions are not optimal for the logical transitions at hand. Also, the first sentence needs a fix in terms of verb consistency. I'd suggest:
"The organization should have taken the blame. /Otherwise/If not/, its leader should have sacrificed himself for the well-being of all."
"She is one of a kind – she displays high empathy on each and every strangers she meets. Although one could say she really lives in a fiction."
"The city is wondrous, in spite of its proximity to my hometown. /To boot/Even more/Also/, a highly regarded culture resides there."