Конь? Colloquial? Oh no. If you speak about kings, knights, (ancient) wars or alike, it's конь and only конь: боевой конь (warhorse), рыцарский конь (knight's horse). And when you have "steed" in English, in Russian it will always be конь.

it means also, yet it never starts off a sentence, it is usually in the middle

парке goes after certain prepositions. Парка goes after certain prepositions and mostly when counterpart sentence in English requires “of“ or Saxon Genitive. Basically you need to learn what “grammatical cases“ are :¬]

And this: http://www.russianforeveryone.com/Rufe/Lessons/Course1/Grammar/GramUnit6/GramUnit6_3.htm

First, look what a grammatical case is: https://en.wikipedia.org/wiki/Grammatical_case – basically different contexts will make the noun in Russian to take different forms (like in English, only more: HE is there → I look at HIM).

Then take a look at the very right top corner of this page: https://ru.wiktionary.org/wiki/%D0%BF%D0%B0%D1%80%D0%BA#.D0.A0.D1.83.D1.81.D1.81.D0.BA.D0.B8.D0.B9

After the preposition в you have to use a form that is called prepositional/locative, market there as Пр.

OK then, I'll try to explain :).
Конь is the most ancient and the most common word. Лошадь appeared quite later and used to mean "a not-so-good horse". That's why you'll generally hear конь when speaking about knights and other riders, and лошадь when speaking about plows, teams of horses and so on. Note though that both of them do not specify the gender of the horse. Yes, конь is grammatically male, and лошадь is grammatically female, but they do not mean a particular gender. This might be so, but only in colloquial speech of urban people :).
To design the genders of horses, you have:

• Жеребец for a stallion
• Кобыла for a mare
• Мерин for a gelding
• Жеребёнок for a foal (or a colt)

See also here (in Russian).

Лошадь is the name of the species, while конь is the male of that species (as opposed to кобыла). Same goes with dog, where Polish “pies” means both the species and the male dog, but Russian distinguishes between собака and пёс, respectively.

Usually longer word = higher register of language.

You probably mean the Prepositional ending. Am I right?

When you use в/на with a noun to say where something is or where something happens the nouns gets changed into its Locative (a.k.a. Prepositional) form. Nouns of most types get an -е ending. Feminine nouns ending in -ь as well as nouns ending in -ия, -ие, -ий get an -и instead. Имя, время also get it (имени, времени).

• школа ——> в школе (in/at school)
• семья ——> в семье
• стол ——> на столе (on a table), в столе (inside one of its drawers)
• яйцо ——> в яйце (in an egg)
• кровать ——> на/в кровати
• лошадь ——> на лошади
• конь ——> на коне (конь is a masculine noun!)
• история ——> в истории (in history)
• лекция ——> на лекции(at a lecture)
• здание ——> в здании (in a building)

Now, in case you wondered what a case is. The form you see in the dictionary is, generally speaking, used when the noun is a grammatical subject of the sentence. A different role requires a different form; prepositions also have their form requirements.

These forms are called cases. Russian system has six of them. English sort of distinguishes between the subject and everything else—but only for pronouns (I/he/she vs. me/him/her)—and also has a possessive form for pronouns (my) and nouns (teacher's). These forms could theoretically have been assigned numbers but in reality they are usually referred by their conventional "names".

The Prepositional case is not the most common one—the Genitive probably is—but its endings are simple (only two options) and its uses are few and focused. It is also the only case that is never used without a preposition (hence the name). Four prepositions use it: в, на, о (об, обо), при.

• and по in a few bookish set expressions.
• by contrast, the Genitive is triggered by over two dozen prepositions and has got numerous other uses. It is a very useful case but you will not master all of it at once.

I don't get what you're talking about but you should have put "Эта лошадь тоже в парке"