The epidein is an infinitive dependent upon epithumeite, i.e. those things which you are desirous to see (=aor.act.inf. of ephoraw).The next bit is really nice Greek - "the Athenians will ressurrect the great power of the city, fallen though it is".
As regards the second passage, the first phrase is simple, "and immediately the water became contaminated", then "but it was drunk (epineto) no less (ouden hsson - adverbial comparative of kakos) together (adverbial homou) with the mud, though it was bloodied (this is the concessive use of the perfect passive participle of haimatow), and it was (hn) fought over (perimachhton - adj. from perimachomai with a passive sense) by (lit. among - en) many [men].
Thus: "And immediately the water became contaminated, but it was drunk nonetheless together with mud, even though it was bloodied, and it was even fought over by many".
Hope this helps,