Customized citation and bibliography style (Estonian)

Question

I'm new to LaTeX and having a hard time with finding the right bibliography and citation style for my paper. (The 'right' style being the style demanded by my university which, unfortunately, is quite strict in that regard.)

What I'm looking for is a style where in-text references look like this:

Earlier works on the topic (see e.g. Sedov 1985, Hristov 2013)...

Hristov (2013: 33) proposes that...

J. Miller (1999: 22) criticizes earlier studies carried out by L. Miller (1970, 1982), ...

That is, the citation should simply consist of the name + year of publication (no coma in between, no brackets around), also with the possibility to cite name and year separately. In addition, there should be a possibility to add the initial(s) of the author's first name(s) to the citation of the surname, in case that there's two or more authors with the same surname.

Apart from that, I'm also looking for a possibility to change some language-specific terms used in the references. That is, I'd like to switch out 'et al.' for the Estonian 'jt' (used in case of three or more authors) and the 'and' or & for the Estonian conjunction 'ja' (in case of two authors):

Miller jt (1997)

Hakulinen ja Karlsson (1979)

Now, when it comes to the bibliography, the general format for articles should look like this:

Surname, First Name Year. Title of article. – Name of journal. Volume. Editor. Place: Publisher, page numbers.

Andrews, Avery 1985. The major functions of the noun phrase. – Language typology and syntactic description. Vol. 1: Clause structure. Ed. by T. Shopen. Cambridge: Cambridge University Press, 62–154.

For books that are part of serial publications, there is no – used (and also no page numbers, of course), but the format is:

Surname, First Name Year. Title of article. Name (and number) of serial publication. Place: Publisher.

Hakulinen, Auli, Fred Karlsson 1979. Nykysuomen lauseoppia. Suomalaisen Kirjallisuuden Seuran toimituksia 350. Jyväskylä: Suomalaisen Kirjallisuuden Seura.

As you can also see from the above example, in case of two authors the bibliography should have the pattern Surname 1, first name 1, first name 2 surname 2 year.

Now, it gets even more tricky when there's three or more authors, no authors at all or the original publication uses a different script (e.g. cyrillic). Considering the following examples:

EKK = Erelt, Mati, Tiiu Erelt, Kristiina Ross 2007. Eesti keele käsiraamat. Kolmas, täiendatud trükk. Tallinn: Eesti Keele Sihtasutus.

Miller jt = Miller, John, James Conner, Liam Smith 1999. Some article title. – Language typology and syntactic description. Vol. 1: Clause structure. Ed. by T. Shopen. Cambridge: Cambridge University Press, 155–200.

Sedov = Cедов, B. 1985. Paнняя этническая история балтов. – Проблемы этнической истории балтов. Тезисы докладов межреспубликанской научной конференции. Pига, 92–95.

EKK is a common abbreviation of Eesti keele käsiraamat and as such also used as in-text reference. Now, ideally I'd have a format that would allow me to add this kind of abbreviations that I could use as references and that would appear in front of the quotation mark in the bibliography. In addition, this quotation mark is also used with three or more authors (where there's jt 'et al.' in the in-text reference) and with publications in a different script (where the latinized name is used for in-text reference, but the original name preserved in the bibliography).

For online references, the link should be at the end of the bibliography entry, followed by Vaadatud DD.MM.YYYY., where I could set the date of retrieval myself:

EKK = Erelt, Mati, Tiiu Erelt, Kristiina Ross 2007. Eesti keele käsiraamat. Kolmas, täiendatud trükk. Tallinn: Eesti Keele Sihtasutus. https://www.eki.ee/books/ekk09/. Vaadatud 26.11.2019.

Now, long story short - do you have any suggestions as to which package to use for citation and bibliography, a package that would already be close to what I'm looking for and also allow for additional modifications? I have tried the apacite package, which is not too bad, however there's so many things I'd have to modify that I wonder if there's something else that might be even closer to what I'm looking for.