2.
(plaque on the bust of the director)
第十一代主任教授
11th chairperson
第【だい】: prefix that makes a number an ordinal
代【だい】: counter for generations (so the 11th successor)
主任教授 : chairperson; compound made of 主任 (しゅにん), person in charge (主=main, 任=obligation) and 教授【きょうじゅ】professor; so the professor in charge (here of the chair of medicine at the Eiroku university, probably)
春日部一郎博士
Dr. Kasukabe Ichirô
春日部 一郎 : his name
博士 : Doctor (title, doctor in title, having done a doctorship) Two readings are possible: はかせ and はくし; this last as a suffix. I don’t know which one is the most likely here…
3. & 4.
(some women setting the busts)
ねえ こんな銅像並べて何が始まるのかしら…
Hee, we are lining those bronze busts, I wonder what will start
銅像 (どうぞう) is bronze statue (lit. bronze-image), but here they are busts
★ 並べる (ならべる) : to line, to put in a row. THe verb is in te-form; and the particle of the object is missing. Probably it has to be interpreted as some kind of cause of the following phrase (we line statues that way, so …)
it is こんな銅像, “such bronze busts”; but it sounds odd in English I think
何が始まる what will start + の (feminine question particle) + かしら feminine speech “I wonder”
ホラあれよーっ 今日は例の永大の…
It's today, that E.U. big thing...
the Japanese original is veeery elliptic, impossible to make a working English in samz order.
ホラ ・ あれ ・ よーっ
bragging ・ that(pr.) ・ [assertion]
今日 ・ は ・ 例の ・ 永大 ・ の…
today ・ [topic] ・ aforementioned ・ Eidai ・ [attribution] …
ホラ : big talk, big thing, bragging
あれよ (that + assertive particle)
例の (れいの) : 1. the usual, 2. that have been told about, aforementioned;
so here 例の永大の(X) is like “the (X) you know of/from Eidai” (the (X) is not stated, but it is obviously the ホラ of the previous phrase)