Yes. Observe the two sentences below.
1) Should I apply for the job again?
2) Should you require more information, please do not hesitate to contact our helpdesk.
Yes, you can start a sentence with "Should," especially when making a recommendation or posing a question.
No it won't, unless it is at the start of a sentence.
No it should not, unless it is at the start of a sentence.
The first word of a new sentence should always be capitalized.
No, unless it is the start of a sentence.
Yes, the word "Example" should be capitalized when used as a proper noun or at the beginning of a sentence.
You can.
No it won't, unless it is at the start of a sentence.
Yes. 'Thus' is another word for 'therefore'. Thus the sentence you start of with 'thus' should be an explanatory sentence.
Yes it should.
It should start with a topic sentence.
No it should not, unless it is at the start of a sentence.
"In conclusion"
no
You start a sentence with whatever word you need to start it with. A sentence can start with "A" if it needs to. A sentence just needs to make sense.
No, only at the start of the sentence.
You did a proper job of it.
Yes, starting a sentence with "but" is acceptable in informal writing for added emphasis or to contrast with the previous idea. However, in formal writing, it is generally best to avoid starting sentences with coordinating conjunctions like "but."