Yes, using that as a noun or an adjective.
Such as:
"That which is truth is believable."
"That car was parked in my driveway."
There are more convoluted forms:
"That all of our efforts failed is extremely disheartening."
yes
yea
It can be, but not all the time.
Yes. Strictly speaking For example at the beginning of a sentence is what is called an "absolute," grammatically unconnected to the rest of the sentence.
Yes, the sentence "his hand is filthy" is grammatically correct.
Yes, it is grammatically correct to begin a sentence with a preposition in certain cases, especially in informal or conversational writing. However, it is generally avoided in formal or academic writing.
Any word that may begin a sentence may begin a paragraph.
"That was wrong" is a grammatically correct sentence.
This sentence is not grammatically correct. For the sentence to be grammatically correct, the space between "in" and "to" would have to be removed. Therefore the sentence should read "They are into skating."
Yes. There is no word that cannot begin an English sentence. But that does not mean that it is always a good way to begin one.
The sentence is grammatically correct.
Yes, it is grammatically correct.