Months are perfectly fair game, as is language in general. You can go as far as you like but you need to give the reader a means of engagement. Some examples:
Names of Months. <PERSON> book "The Wake" is largely written in (greatly simplified) old English. The language is modified enough so that it gives the flavour of Old English while being phonetically similar enough to modern English that the reader can easily enough pick up the flow and understand what is written. The names of months are different (for example, July is 'Weodmonth') but they are descriptive names and their meaning is amplified by context (the protagonist / narrator of the novel mentions that July / Weodmonth is a month when weeds may rapidly spread among crops without lots of weeding effort). In a different genre, the Elder Scrolls series of RPGs has a set of months with descriptive names (Morning Star, Sun's Dawn, First Seed, Rain's Hand, Second Seed, Mid Year, Sun's Height, Last Seed, Hearthfire, Frost Fall, Sun's Dusk, Evening Star): in context it's fairly obvious not just that these are the names of months but which parts of they ear they might refer to.
Language, more broadly. See the previous <PERSON> example, also <PERSON> novel "Feersum Endjinn", large parts of which are written in a sort of phonetic Glaswegian. 873
In this type of book the entire story, or large sections of it, is written in the made-up languade. In both cases there is just enough phonetic similarity to English that the reader can engage with the content.
On the other hand, some writers invent entire languages for their stories. I guess the archetype for this is <PERSON>. A useful device here is the "common tongue" which is written in the book as English. So when <PERSON> reads the inscription on the One Ring in Black Speech, he says "Ash nazg durbatulûk, ash nazg gimbatul, ash nazg thrakatulûk agh burzum-ishi krimpatul. Translated, the words mean 'One ring to rule them all, one ring to find them, one ring to bring them all and, in the darkness, bind them." So the reader gets a flavour of the invented language but the wizard's explanation to <PERSON> of the meaning in the common tongue also serves as an explanation to the reader.
You seem particularly keen on the worldbuilding aspects and that's fine - consider <PERSON> again. His primary concern was worldbuilding and linguistics, the novels were almost a by-product of this. It shows in the vast amount of detail in the Appendices in The Lord of the Rings, and in the huge amount of detailed world building he put into his languages (Quenya and Sindarin are sufficiently well developed that it is possible to learn to speak them, albeit the vocabulary is not broad enough to use the languages in everyday speech) and his world building (the amount of detailed little pieces that he wrote about Middle Earth but never made much effort to publish, which were later assembled by his son into the Silmarillion). So if that's your thing, just enjoy it - if a novel happens to fall out of your world building then that's great, but it's perfectly legitimate to enjoy world building for its own sake.
<PERSON>. 88