ALLEGED QUOTE: "It will sometimes be necessary to use falsehood for the benefit of those who need such a mode of treatment." or "That it is necessary sometimes to use falsehood as a medicine for those who need such an approach." The Preparation of the Gospel
The work in question may be found here as the title to the 31st chapter. However, these words are not apart of Eusebius' original works- they were added later most likely by a medieval translator. Literary works of antiquity, such as The Preparation of the Gospel, were not divided into chapters or paragraphs. In fact, they also no had spacing in between words or even punctuation. It appears whoever divided Eusebius' works into chapters read the text and assigned chapter titles according to the material's content. The actual text of the "chapter" in question is as follows:
"[PLATO] 'But even if the case were not such as our argument has now proved it to be, if a lawgiver, who is to be of ever so little use, could have ventured to tell any falsehood at all to the young for their good, is there any falsehood that he could have told more beneficial than this, and better able to make them all do everything that is just, not by compulsion but willingly? [Cleinias] 'Truth, O Stranger, is a noble and an enduring thing; it seems, however, not easy to persuade men of it.' [Plato] Now you may find in the Hebrew Scriptures also thousands of such passages concerning God as though He were jealous, or sleeping, or angry, or subject to any other human passions, which passages are adopted for the benefit of those who need this mode of instruction."
In the above passage, Eusebius is criticizing and citing Plato's dialogue with Cleinias from Plato's work the Laws. Eusebius is neither commanding nor condoning the spread of falsehood.
CONCLUSION: The chapter title in question was not written by Eusebius. It is most likely a late interpolation by a medieval translator for the convenience of reference. The actual text of the chapter was a citation from Plato's works and Eusebius was actually rebuking of those who distort facts in order to gain followers or make a point.
ALLEGED QUOTE: "I have repeated whatever may rebound to the glory, and suppressed all that could tend to the disgrace of religion."
This quote is usually cited as being found in Eusebius' The Preparation of the Gospel Book 12, Chapter 31 (See: here). However, this is the location of the quote we just examined above so we know the quote is not found there. This quote has now been traced back to Edward Gibbon, an 18th century historian, in his work The History of the Decline and Fall of the Roman Empire. The following is found in this work, on page 178:
"The gravest of the ecclesiastical historians, Eusebius himself, indirectly confesses that he has related whatever might redound to the glory, and that he has suppressed all that could tend to the disgrace, of religion."
CONCLUSION: This statement was never made by Eusebius nor does is appear anywhere within his works. For more on this topic, here is an article which traces this quote's origin in depth.
ALLEGED QUOTE: "Eusebius claims he was an eyewitness to the martyrs who were unmolested by attacking wild beasts. He says the beasts 'were stopped short as if by some divine power, and then retreated to the starting point.'"
Though Eusebius records the deaths of many Christian martyrs, I cannot find this statement in any of his works. The quote is said to come from his Ecclesiastical History Book VIII, Chapter VIII. However, the passage in question (See: here) is as follows:
Such was the conflict of those Egyptians who contended nobly for religion in Tyre. But we must admire those also who suffered martyrdom in their native land, where thousands of men, women, and children, despising the present life for the sake of the teaching of our Saviour, endured various deaths. Some of them, after scrapings and rackings and severest scourgings, and numberless other kinds of tortures, terrible even to hear of, were committed to the flames. Some were drowned in the sea, some offered their heads bravely to those who cut them off, some died under their tortures, and others perished with hunger. And yet others were crucified, some according to the method commonly employed for malefactors. Others yet more cruelly, being nailed to the cross with their heads downward, and being kept alive until they perished on the cross with hunger.
Conclusion: This "eye witness" account of Eusebius simply does not seem to exist.