Cleon, your Tagalog is good enough that we can understand what you are saying.  My basis for making the corrections is the assumption that you’d like to fine-tune your ability to communicate in Tagalog.  Generally, your mistakes are minor, but I will try to point them out to you to help you understand better the Tagalog sentence structures.  Also, your entry is relatively long and would therefore take me more time to go through the whole thing.  Will do therefore it in installments.  OK ba, pare?  :-) 

Moi moi ang ungoy

“Ng” is one of the letters in our alphabet and it has its own sound, i.e., you can’t separate the sound of the “n” from the “g”.  Therefore, since I assume you know the pronunciation of the Tagalog word for “monkey”, it should be written as “unggoy”, where you need the extra “g” to give it its own sound.

I would also say that the more correct way of writing your title would be: “Moi moi – ang unggoy”.  That’s because, as you wrote it, it would sound or seem like “moi moi” is the predicate, even if we know it isn’t.   Should you want to express it as a sentence, it would be: “Ang unggoy na si Moi moi” or “Si Moi moi na unggoy”.  

Noong dati, ako nagtrabaho bilang US Marine sa Timog Pilipinas.

You don’t really need the “noong” since “dati” would suffice to refer to a period in the past.  “Noong” alone is used to point to a more specific time in the past.  We normally say “noong dati” when we are comparing something in the past with another in the present.  In such a case, the “noong” serves to add emphasis to the difference being made with the comparison.

“Dati kaunti lang ang tao sa Pilipinas.” = Before, there were just a few/not too many people in the Philippines.

“Noong panahon ng WW2, kaunti pa rin ang tao sa Pilipinas.” = During the WW2 period, there were still a few people in the Philippines.

“Noong dati/Dati kaunti lang ang tao sa Pilipinas, pero ngayon mahigit 100-million na. = Before, there were just a few people in the Phils., but now there are already more than a 100-million.  (The option to add “noong” is just to make the comparison more emphatic.)

“Noon” (without the “g”), may be used in place of “dati”as it also means “before/then/in the past”.  “Dati” though has the additional meaning of “formerly”.    

“Dati/Noon, ako AY nagtrabaho bilang ISANG US Marine sa ... = Before, I worked as a US Marine in/at...  (In Tagalog, the comma before “ako” is optional.  If the subject comes before the predicate, you need an “ay” to link them.  You will also need to add “isa+ng” for the English “a” before US Marine.  Without that “isang”, what you said is that YOU WERE the US Marine.  Astig mo, pare! :-)

Other ways to begin your sentence:

Dati/Noon, nagtrabaho ako bilang isang...

Nagtrabaho ako dati/noon bilang isang...

Moi moi, ang unggoy (Tagalog)

Noong dati - ( This one could be just Dati only or Nuon only), ako ay nagtrabaho bilang US Marine sa parteng Timog ng Pilipinas. (Di ko pwedeng sabhin kung saan ito eksakto), pero sa mga oras na yun yung walang trabaho ( at dami naman ganyan ), paminsan minsan binisitahin ko ang maliit na ungoy unggoy ng Philippine Marines. Cute na cute naman siya. As in( can be Grabe which means super like you really find that monkey so cute). Cute. Ang Pangalan niya ay si Moi Moi.

Pero pagkatapos ang nang panahon ko nakasama kasama ko siya, ayaw ko pa ang mga unggoy. Para sa akin kasi ako ay Amerikano at wala namang unggoy sa USA, napakainteresante yung mga unggoy. Pero ngayon, si Moi Moi kasi, ako nanamuhi ng mga ungoy( I'm not sure one you mean by nanamuhi or is it namumuhi, not sure).

Mas gusto ko ang mga aso. Gusto talaga nilang ipasaya mapasaya ka. Pero ang unggoy, walang paki alam.

Unggoy, sa akin lang, katulag  katulad ng mga anak nanggaling sa kapamilya mo napakasama at bastos. Okay naman sila pag nagbibisita ng isang o dalawang oras na lang, pero pagkatapos yun nun kailangan na silang nilang umuwi.

Mas gusto ko mga aso.  -> Mas gusto ko ang mga aso = I prefer dogs.

Gusto talaga nilang ipasaya ka. -> Gusto talaga nilang pasayahin ka. = They really like to make you happy.

“ipa” is used with a verb to relay a command through a second person for a third person, i.e., person A asks B to tell C to do something.    

“ipasara” = to have something closed by someone else

“ipatapon” = to have something thrown away by someone else.

Mary: Peter, ipasara mo kay Paul ang bintana. = Peter, tell Paul to close the window.

Paul: Peter, ipatapon mo kay Mary ang basura. = Peter, tell Mary to take out the garbage.

Since “saya” (happiness) is a noun, you can’t use “ipa” with it.  You use the “pa – hin/in” combination instead, which is also used with some verbs.

“pasayahin” = to make someone happy

“pagandahin” (ganda = beauty) = to make something/someone look pretty.

“patakbuhin” (takbo = run) = to make something/someone run.

Pero ang unggoy, walang pakialam.  = But a monkey shows no concern.

Ang (mga) unggoy, sa akin lang, ay katulad ng (mga) anak... = A monkey (Monkeys), just in my opinion, are like a child (children)...  

... nanggaling kapamilya mo napakasama at bastos.  (As it is, it translates to, “coming from your co-family wicked and rude”.)

Maybe what you meant is this:  Ang mga unggoy, sa akin lang, ay katulad ng mga anak na napakasama at bastos ng kamag-anak mo. = Monkeys, just in my opinion, are like the wicked and rude children of your relatives.  

"Kamag-anak" is the word for relatives.

Okay naman sila pag nagbibisita ng isang o dalawa oras na lang, pero pagkatapos yun kailangan silang umuwi. ->  Okay naman sila pag bumibisita ng isa o dalawang oras lang, pero pagkatapos noon/nun kailangan na silang umuwi. = They are all right when visiting just for one or two hours, but after that they need to go home.

“nagbibisita” – the act of visiting (usually a third person or persons)
“bumibisita” – visits/visiting
Ang doctor ay nagbibisita ng kanyang mga pasyente sa ospital = The doctor visits his patients in the hospital.
Si John ay bumibisita sa amin araw-araw. = John visits us every day.

Para sa akin, kasi ako AY Amerikano at wala namang unggoy sa USA, napakainteresante yung/ang mga unggoy. = For me, because/since I am an American and there are no monkeys in the USA, those/the monkeys are very interesting.

“Ako”is followed by “ay” when used as a subject before the predicate.

Ako ay Amerikano = Amerikano ako = I am an American.   

Pero ngayon, si Moi Moi kasi, ako nanamuhi ng mga ungoy.

Though we understand that by “si Moi Moi kasi” you meant “because of Moi Moi”, we would say it as “dahil kay Moi Moi” instead.  Your “si Moi Moi kasi” would translate more as “as it is Moi Moi’s fault” when used in this sentence.

Ako AY namumuhi SA mga unggoy = I detest monkeys.  (I would consider “namumuhi” (root is “muhi”) as too strong a word to use here unless you now truly abhor monkeys.  But if it’s just a simple dislike, you may say “ayaw ko na sa mga unggoy”.

Pero ngayon, dahil kay Moi Moi, ako ay namumuhi sa mga unggoy/ayaw ko na sa mga unggoy” = But now, because of Moi Moi, I abhor monkeys/I don’t like monkeys anymore.