I looked up 眺む in a 古文 dictionary and got 「ぼんやりと見やる。（ぼんやりと）物思いに沈む」, so it seems you’re correct here. In that case though, it could be that the modern translation just excluded つくづくと because the meaning was already included in 眺む haha
This is a meaning I did not find in the dictionary. Does that mean in this specific poem or maybe poetry in general?
Grammar is not really my strong suit, but I’ll give it a try. I think it just means 色がない but with more emphasis. As you said, ということ can be nominalization, but in this case it sounds like it just emphasizes 色. For example if I wanted to say “That person doesn’t have a clue about ethics,” I could write その人は倫理ということを知らない. Without ということ, it would just be “That person doesn’t know ethics.” In a similar vein, the も just gives a sort of flavor of “even,” so maybe putting it all together (rather wordily), it becomes “There wasn’t even a single color to be seen.” I’m sure there’s plenty of ways to write that more concisely, but I’m even worse at poetry in English 
Thanks for pointing this out! I only knew 郭公 as the little ol cuckoo, but it turns out there’s another bird associated with it. Looking into this further, I came across the following entry:
[語誌]中国では①[カッコウ科の鳥] を指す語として用いられているが、日本では平安初期の「新撰万葉」「新撰字鏡」などが、「ほととぎす」に「[郭公鳥] (郭公鳥(かっこどり)とは？ 意味や使い方 - コトバンク)」「郭公」などの字をあてており、長く「ほととぎす」を表記する語として用いられてきた。「かっこう」を「郭公」と表記するようになるのは近代に入ってからである。
So basically the Heian period Japanese used that kanji for the cuckoo, and then later it was used as an ateji for the カッコウ科 birds. Given that the cuckoo has the esteemed position of having at least 17 different ways to express its name in kanji, I guess it’s only natural it would have to share some with other birds later on!
It seems like most attribute the tears to the poet, and he’s pleading with the cuckoo to not make him add his tears to the rain. Grammatically I imagine it’s ambiguous, as the poem follows the tradition of plopping a noun at the end and leaving it there for 詠嘆. But if we were to look for clues, I’d say that since the beginning starts with 「昔思ふ」, the following would still be in relation to him. In my opinion, it’s too sudden a shift to be reminiscing on one’s glory days while staying in a shabby hut in the rain and then switch focus to the bird. The bird is just another part of the scenery that adds to his sorrow.